REESE  LIBRARY 

OK  THE 

UNIVERSITY  OF  CALIFORNIA. 

Deceived  ,  igo     . 

Accession  No .          830  .(>  .L   Class  No . 


HARPER'S  SCIENTIFIC  MEMOIRS 

EDITED  BY 

J.  S.  AMES,  PH.D. 

PROFESSOR    OF    PHYSICS    IS    JOHNS    HOPKINS    UNIVERSITY 


IV. 

I 

THE    MODERN    THEORY    OF    SOLUTION 


THE    MODERN 
THEORY    OF    SOLUTION 


MEMOIRS  BY  PFEFFER,  VAN'T  HOFF 
ARRHENIUS,  AND  RAOULT 


TRANSLATED  AND  EDITED 

BY   HARRY    C.  JONES,  PH.D. 

ASSOCIATE    IS    PHYSICAL    CHEMISTRY    IN    JOHNS    HOPKINS    UN1VEUSIT* 


NEW   YORK  AND  LONDON 

HARPER     &     BROTHERS    PUBLISHERS 
1899 


HARPER'S    SCIENTIFIC   MEMOIRS. 

EDITED    BY 

J.    S.  AMES,  PH.D., 

rilOFKSSOK   OF   P11YSIOS    IN   JOHNS   J1OPKINB  UNIVKK61TY. 


READY: 

THE   FREE   EXPANSION   OF  GASES.      Memoirs 

by  G;iy-Lussac,  Joule,  and   Joule  ;uul  Thomson. 

Editor,    Prof.  J.   S.   AMISS,   Ph.D.,  Johns    Hopkins 

University.    75  cents. 
PRISMATIC     AND     DIFFRACTION      SPECTRA. 

Memoirs  by  Joseph  von  Fraunhofer.     Editor,  Prof. 

J.    S.    A MICS,    Ph.D.,    Johns    Hopkins    University. 

00  cents. 
RONTGKN   RAYS.    Memoirs  by    Rontgen,   Stokes, 

and    J.   J.     Thomson.     Editor,    Prof.    GKOKGK    F. 

B  A  UK  KB,  University  of  Pennsylvania. 
THE    MODERN    THEORY    OF    SOLUTION.      Me- 
moirs by  Pfeffer,  Van'r.  Hoff,  Arrhenins,  and  Raonlt. 

Editor,  Dr.  II.  C.  JONKS,  Jolins  Hopkins  University. 

IN  PREPARATION: 

THE  LAWS  OF  GASES.  Memoirs  by  Boyle  and 
Ainnga  t.  Editor,  Prof.  C  A  uuBAitrs,  BrownUniversity. 

THE  SECOND  LAW  OF  THERMODYNAMICS. 
Memoirs  by  Carnot,  Clausing,  and  Thomson.  Editor, 
Prof.  W.  F.  MAGIK,  Princeton  University. 

THE  PROPERTIES  OF  IONS.  Memoirs  by 
Kohlransch  and  Hittorf.  Editor,  Dr.  II.  M.  GOOD- 
WIN, Massachusetts  Institute  of  Technology. 

THE  FARADAY  AND  ZEEMAN  EFFECT.  Me- 
moirs by  Faradav,  Kerr,  and  Zeeman.  Editor,  Dr. 
E.  P.  LKWIS,  University  of  California. 

WAVE-THEORY  OF  LIGHT.  Memoirs  by  Younjr 
and  Fresnel.  Editor,  Prof.  HENRY  CIIF.W,  North- 
western University. 

NEWTON'S  LAW  OF  GRAVITATION.  Editor, 
Prof.  A.  S.  MAOKKNZIK,  Bryn  Mawr  College. 

NEW    YORK    AND    LONDON: 
HARPER  &  BROTHERS,  PUBLISHERS. 


Copy  right,  1899,  by  HAUTEI:  &  BUOTIIKKB. 


All  rights  reserved. 


PREFACE 


IT  is  well  known  that  great  progress  has  been  made  in  phys- 
ical chemistry  daring  the  last  ten  or  fifteen  years.  Indeed, 
this  has  been  of  such  a  character  that  what  is  now  studied 
and  taught  under  the  head  of  physical  chemistry  differs  fun- 
damentally from  what  was  included  under  that  subject  a  few 
decades  ago. 

The  papers  in  this  volume  have  been  selected  and  arranged 
with  the  idea  of  showing  how  the  two  leading  generalizations, 
which  underlie  these  recent  developments,  have  been  reached. 
Previous  to  1885,  physical  chemistry  dealt  chiefly  with  the 
physical  properties  of  chemical  substances,  and  the  relations 
between  properties  and  composition  on  the  one  hand,  and  prop- 
ertiejs  and  constitution  on  the  other.  How  would  the  differ- 
ence in  composition  of  an  oxygen  atom,  or  a  CH2  group,  affect 
the  physical  properties,  or  what  would  be  the  effect  of  an  oxygen 
atom  united  to  hydrogen  with  respect  to  an  oxygen  atom  united 
to  carbon,  were  questions  which  investigators  were  endeavoring 
to  answer. 

The  first  important  advance  was  made  possible  by  the  work 
of  the  botanist  Pfeffer.  He  undertook  to  investigate  the  os- 
motic pressure  which  solutions  of  substances  exert  against  the 
pure  solvent.  His  work,  which  was  published  in  an  extensive 
monograph,  Osmotische  Untersuchungen,  was  carried  out  pure- 
ly from  a  physiological-botanical  stand-point,  and  Pfeffer  did 
not  indicate  its  bearing  upon  any  physical  -  chemical  prob- 
lem. Enough  of  his  work  is  given  to  show  the  method  which 
he  used  and  the  apparatus  which  he  employed.  He  worked 
with  solutions  of  several  substances  in  water,  but  from  our 
point  of  view  it  is  important  to  note  that  he  worked  with  dif- 
ferent dilutions  of  the  same  substance  in  the  same  solvent,  and 


83061 


PREFACE 

also  determined  the  temperature  coefficient  of  osmotic  press- 
ure. Just  enough  of  his  results  are  given  to  bring  out  these 
two  important  points. 

The  paper  of  Van't  Hoff,  given  in  full  in  this  volume,  was 
published  in  the  first  volume  of  the  ZeitscJirift  fur  Physika- 
UscJie  Chemie  in  1887.  In  this,  the  relation  between  dilute 
solutions  and  gases  was  pointed  out  for  the  first  time.  The 
law 'of  Boyle  for  gas-pressure  was  found  to  be  applicable  to  the 
osmotic  pressures  of  solutions  of  different  concentrations. 
That  osmotic  pressure  is  proportional  to  concentration  was 
found  to  be  true  from  the  results  of  Pfeffer's  investigations. 
This  was  the  first  important  generalization  showing  the  rela- 
tion between  gases  and  dilute  solutions. 

Van't  Hoff  showed,. further,  from  Pfeffer's  results,  as  well  as 
theoretically,  that  the  law  of  Gay-Lussac  for  the  temperature 
coefficient  of  gas  -  pressure,  applies  to  the  temperature  coef- 
ficient of  osmotic  pressure,  which  was  the  second  important 
step.  Then  Van't  Hoif  took  another  and  even  more  important 
step,  showing  that  the  osmotic  pressure  of  a  dilute  solution  is 
exactly  equal  to  the  gas-pressure  of  a  gas  at  the  same  temper- 
ature, containing  the  same  number  of  molecules  in  a  given 
space  as  there  are  molecules  of  dissolved  substance.  Thus, 
two  grams  of  hydrogen  (H^  =  2)  will  exert  a  gas-pressure  in  a 
space  of  a  litre  which  is  exactly  equal  to  the  osmotic  pressure 
which  three  hundred  and  forty  -  two  grams  of  cane  -  sugar 
(C12H220U  =  342)  will  exert  in  a  litre  of  aqueous  solution. 
From  this,  the  law  of  Avogadro  for  gases  applies  at  once  to 
dilute  solutions,  and  we  can  then  say  that  solutions  having 
the  same  osmotic  pressure,  at  the  same  temperature,  contain 
the  same  number  of  ultimate  parts  in  unit  space. 

Thus,  the  three  fundamental  laws  of  gas-pressure  apply  to 
the  osmotic  pressure  of  dilute  solutions,  and  we  are  therefore 
justified  in  attempting  to  apply  other  laws  of  gases  to  dilute 
solutions.  We  have  said  dilute  solutions,  and  have  thus  in- 
dicated that  the  gas  laws  would  not  apply  to  concentrated  so- 
lutions. This  is  true,  and  in  this,  again,  solutions  are  analo- 
gous to  gases,  since  the  ordinary  gas  laws  do  not  apply  to  very 
concentrated  gases — i.e.,  gases  near  the  point  of  liquefaction. 

But  if  the  laws  of  gas-pressure  apply  to  the  osmotic  pressure 
of  dilute  solutions,  then  we  would  naturally  ask  if  any  excep- 
tions to  the  laws  of  gas-pressure  find  their  counterpart  in  the 


PREFACE 

osmotic  pressure  of  solutions.  We  'know  that  certain  vapors, 
as  that  of  ammonium  chloride,  exert  a  greater  pressure  than 
they  would  be  expected  to  do  from  Avogadro's  law.  These 
vapors,  then,  are  exceptions  to  the  gas  laws. 

We  find  their  strict  analogues  in  the  osmotic  pressures  of 
certain  solutions.  The  laws  of  gas-pressure  apply  to  the  os- 
motic pressures  of  dilute  solutions  of  substances  of  the  class 
of  cane-sugar  —  i.  e.,  those  substances  whose  solutions  do  not 
conduct  the  electric  current.  As  quickly  as  we  turn  to  solu- 
tions of  the  strong  acids  and  bases,  and  salts,  we  find  that  all 
of  them,  when  dissolved  in  water,  exert  an  osmotic  pressure 
against  the  water  which  is  greater  than  would  be  calculated 
from  the  concentration.  Just  as  the  vapor-pressure  of  ammo- 
nium chloride  is  abnormally  large,  so  the  osmotic  pressure  of 
solutions  of  substances  such  as  those  named  above  is  abnor- 
mally large.  The  gas  laws  not  only  apply  to  the  osmotic  press- 
ure of  solutions,  but  just  as  there  are  exceptions  to  these 
laws  in  gas-pressure,  so,  also,  there  are  exceptions  in  osmotic 
pressure. 

What  is  the  explanation  of  these  apparent  anomalies  ?  This 
phenomenon  was,  for  a  long  time,  unexplained  for  gases.  It 
was  pointed  out  that  here  were  exceptions  to  the  law  of  Avoga- 
dro,  and  this  law  could,  therefore,  not  be  generally  applicable. 
But  the  anomalies  were  finally  accounted  for  with  gases  by 
showing  that  vapors  like  those  of  ammonium  chloride  disso- 
ciated or  broke  down  into  constituent  parts,  the  amount  of  the 
dissociation  depending  in  part  upon  the  temperature.  That 
the  vapor  of  ammonium  chloride  is  partly  broken  down  into 
ammonia  and  hydrochloric  acid  was  shown,  in  a  perfectly  sat- 
isfactory manner,  by  the  work  of  Pebal  and  others. 

But  of  what  aid  was  this  explanation  for  anomalous  gas- 
pressure,  in  ascertaining  the  cause  of  the  abnormal  osmotic 
pressure  of  dilute  solutions  of  acids,  bases,  and  salts  ?  It  was 
simple  enough  to  conceive  of  a  molecule  of  ammonium  chloride 
being  broken  down  by  heat  as  follows  : 


especially  after  it  had  been  proven  experimentally  that  the 
vapor  of  ammonium  chloride  contains  both  free  ammonia  and 
free  hydrochloric  acid  ;  and  this  increase  in  the  number  of 
parts  present  would  explain  the  abnormally  large  gas-pressure, 
and  still  allow  the  law  of  Avogadro  to  be  generally  applicable. 

vii 


PREFACE 

But  could  we  conceive  of  any  analogous  explanation  for  the 
abnormal  osmotic  pressures  ?  How  could  water  break  down 
stable  compounds,  such  as  the  strong  acids  and  bases  ?  Ar- 
rhenius  explained  these  abnormal  osmotic  pressures  in  a  paper 
published  also  in  the  first  volume  of  the  Zeitschrift  fur  Pliysi- 
kalische  Chemie,  and  which  is  also  given  in  full  in  this  volume. 
According  to  him,,  those  substances  which  give  abnormally 
large  osmotic  pressures  are  broken  down  in  solution,  not  into 
molecules  as  ammonium  chloride  is  broken  down  into  molecules 
by  heat,  but  into  ions,  which  are  atoms,  or  groups  of  atoms, 
charged  with  electricity.  It  is  very  important  in  this  connec- 
tion to  distinguish  between  atoms  and  ions.  A  compound  like 
potassium  chloride  is,  according  to  Arrhenius,  broken  down,  or, 
as  he  would  say,  dissociated  into  potassium  ions  and  chlorine 
ions,  which  exist  in  the  presence  of  water.  If  a  potassium  ion 
had  properties  at  all  similar  to  a  potassium  molecule  the  sug- 
gestion of  Arrhenius  would  be  absurd,  since  it  is  well  known 
how  vigorously  ordinary  potassium  acts  upon  water,  while 
potassium  chloride  dissolves  in  water  without  any  such  action. 
The  fundamental  distinction  between  molecules  and  ions  is 
that  the  latter  are  charged  either  positively  or  negatively,  and 
by  virtue  of  their  charge  do  not  have  properties  similar  to  those 
of  the  molecules. 

This  assumption,  that  the  molecules  of  those  substances 
which  give  abnormally  large  osmotic  pressures  are  broken 
down  in  solution  into  a  larger  number  of  parts,  if  true,  shows 
that  the  law  of  Boyle  holds  for  the  osmotic  pressure  of  all 
dilute  solutions — i.  e.,  the  osmotic  pressure  is  proportional  to 
the  number  of  parts  present.  In  the  case  of  those  substances 
whose  solutions  do  not  conduct  the  current — non-electrolytes — 
the  molecules  exist  in  solution  as  such,  and  each  exerts  its  own 
definite  osmotic  pressure.  But  in  solutions  of  those  substances 
which  conduct  the  current,  at  least  some  of  the  molecules  are 
broken  down  into  ions,  the  number  depending  upon  the  dilu- 
tion, and  each  ion  exerts  just  the  same  osmotic  pressure  as  a 
molecule.  Since  a  molecule  cannot  break  down  into  less  than 
two  ions,  those  substances  whose  solutions  are  even  partly  dis- 
sociated into  ions  must  exert  greater  osmotic  pressure  than 
those  whose  solutions  are  completely  undissociated. 

The  suggestion  that  solutions  of  electrolytes  contain  ions 
which  conduct  the  current  is  not  new  with  Arrhenius. 


, 


PREFACE 

Grotthuss  attempted  to  explain  how  the  current  is  able  to  pass 
through  a  solution  of  an  electrolyte,  and  Clausius  assumed 
the  presence  of  free  ions  in  electrolytic  solutions.  The  chem- 
ist Williamson,  as  the  result  of  his  now  classic  synthesis  of 
ether,  also  concluded  that  molecules  of  substances  are  broken 
down  in  solution.  But  the  application  of  electrolytic  dissocia- 
tion, as  it  is  called,  to  explain  the  abnormally  large  osmotic 
pressures  of  electrolytes,  we  owe  to  Arrhenius.  And  what  is 
even  more  important,  he  did  not  simply  assume  that  solutions 
of  electrolytes  are  partly  broken  down  or  dissociated  into  ions, 
but  showed  how  the  amount  of  such  dissociation  could  be 
measured  quantitatively. 

It  was  found  that  those  substances  which  give  abnormally 
large  osmotic  pressures,  give  abnormally  great  depressions  of 
the  freezing-point  of  the  solvent,  and,  further,  solutions  of 
such  substances  conduct  the  current.  Arrhenius  showed  that 
if  the  assumption  of  electrolytic  dissociation  to  account  for 
abnormally  large  osmotic  pressures  was  true,  then  it  must 
also  account  for  the  abnormally  large  depressions  of  the  freez- 
ing-point. The  amount  of  dissociation  of  a  given  solution,  cal- 
culated from  its  osmotic  pressure,  should  then  agree  with  the 
dissociation  calculated  from  the  lowering  of  the  freezing-point. 
But  since  direct  measurements  of  osmotic  pressure  will  be  seen 
from  Pfeffer's  work  to  be  difficult,  this  comparison  could  not 
be  made  directly. 

But  if  Arrhenius's  theory  of  electrolytic  dissociation  is  true, 
then  it  must  account  for  the  property  of  solutions  to  conduct 
the  current;  and  since  conductivity  is  due  only  to  ions,  the 
amount  of  conductivity  could  be  used  to  measure  the  amount 
of  dissociation.  Arrhenius  did  not  compare  the  dissociation 
as  calculated  from  the  freezing-point  lowerings,  directly  with 
that  calculated  from  conductivity,  but  compared  the  values  of 
it  certain  coefficient,  i,  obtained  by  the  two  methods  for  a  large 
number  of  substances,  and  found  a  striking  agreement  through- 
out. This  agreement,  then,  made  it  probable  that  the  theory 
of  electrolytic  dissociation  corresponds  to  a  great  truth  in  nat- 
ure, and  that  the  analogy  between  solutions  and  gases  is  even 
more  deeply  seated  than  was  at  first  supposed. 

It  is  impossible  to  show  here  the  wide-reaching  significance 
of  this  analogy,  and  of  the  theory  of  electrolytic  dissociation. 
This  would  require  a  fairly  comprehensive  survey  of  the  field  of 

ix 


PREFACE 

physical  chemistry.  Suffice  it  to  say  here  that  all  of  the  more 
important  advances  in  physical  chemistry  during  the  last  ten 
or  twelve  years  have  centred  around  these  two  generalizations, 
which  may  be  termed  the  corner  -  stones  of  modern  physical 
chemistry. 

It  has  already  been  stated  that  those  substances  which  give 
abnormally  large  osmotic  pressures,  give  abnormally  great  de- 
pressions of  the  freezing-point  of  the  solvent.  This  brings  us 
to  the  work  of  Raoult  on  the  freezing-point  depression,  and 
lowering  of  vapor-tension,  of  solvents  by  substances  dissolved 
in  them.  Three  of  the  more  important  papers  of  Raoult  along 
these  lines  are  given  in  this  volume. 

Raoult  showed  that  the  depression  of  the  freezing-point  of  a 
solvent,  or  of  its  vapor-tension,  depends  upon  the  relation  be- 
tween the  number  of  molecules  of  solvent  and  of  dissolved  sub- 
stance. He  showed  from  this  how  it  was  possible  to  determine 
the  unknown  molecular  weights  of  substances,  by  determining 
how  much  a  given  weight  of  the  substance  would  lower  the 
freezing-point,  or  lower  the  vapor-tension,  of  a  given  weight  of 
a  solvent  in  which  it  was  dissolved.  These  methods,  the  theo- 
retical development  of  which  we  owe  to  Raoult,  have  been 
greatly  improved  by  others  from  an  experimental  stand-point, 
and  have  been  very  widely  applied,  especially  to  the  determina- 
tion of  the  molecular  weights  of  substances.  It  should  be  es- 
pecially mentioned  that  the  method  of  measuring  the  depres- 
sion of  the  vapor-tension  has  been  almost  entirely  supplanted 
by  the  method  of  determining  the  temperature  at  which  solvent 
and  solution  boil.  From  the  rise  in  the  boiling-point  of  the 
solvent  produced  by  the  dissolved  substance  we  can  calculate 
the  molecular  weight  of  the  latter.  This  improvement  on  the 
Raoult  method  of  measuring  the  depression  in  vapor- tension 
we  owe  to  Beckmann. 

The  freezing-point  method  especially  has  now  been  improved 
until  it  can  be  also  used  as  a  fairly  accurate  measure  of  elec- 
trolytic dissociation.  And  it  can  be  stated  that  electrolytic 
dissociation,  measured  by  the  freezing-point  method,  agrees 
within  the  limits  of  experimental  error,  with  that  measured  by 
the  conductivity  method. 

The  following  papers  will  show,  then,  how  the  analogy  be- 
tween dilute  solutions  and  gases  was  first  recognized  and  point- 
ed out,  and  how  the  theory  of  electrolytic  dissociation  arose  to 


PREFACE 

account  for  the  abnormal  results  obtained  with  electrolytes — 
abnormally  large  osmotic  pressures,  depressions  of  freezing- 
point,  and  depressions  of  vapor-tension. 

Since  the  theory  was  proposed  it  has  been  tested  both  theo- 
retically and  experimentally  from  many  sides;  with  the  result 
that,  when  all  of  the  evidence  available  is  taken  into  account, 
the  theory  of  electrolytic  dissociation  seems  to  be  as  well  es- 
tablished as  many  of  our  so-called  laws  of  nature. 

HARRY  C.  JONES. 
Johns  Hopkins  University. 


GENERAL    CONTENTS 


PAGH 

Preface v 

Osmotic  Investigations.  [Selected  Sections.]  By  W.  Pfeffer 3 

Biography  of  Pfeffer 10 

The  Role  of  Osmotic  Pressure  in  the  Analogy  between  Solutions  and 

Gases.  By  J.  H.  Van't  Hoff 13 

Biography  of  Van't  Hoff 42 

On  the  Dissociation  of  Substances  Dissolved  in  Water.  By  S. 

Arrhenius 47 

Biography  of  Arrhenius 66 

The  General  Law  of  the  Freezing  of  Solvents.  By  F.  M.  Raoult 71 

On  the  Vapor-Pressure  of  Ethereal  Solutions.  By  F.  M.  Raoult 95 

The  General  Law  of  the  Vapor-Pressure  of  Solvents.  By  F.  M.  Raoult.  125 

Biography  of  Raoult 128 

Bibliography 129 

Index..  <&.^..  ...  133 


OSMOTIC   INVESTIGATIONS 

BY 

DR.   W.    PFEFFER 

Pj-ofessor  of  Botany  in  the  University  of  Leipsic 


SELECTED  SECTIONS 


CONTENTS 

PAGK 

Preparation  of  the  Cells 3 

Measurement  of  the  Pressure 7 

Experimental  Results 9 


OSMOTIC    INVESTIGATIONS* 

BY 

DR.    W.    PFEFFER 


SELECTED   SECTIONS 


A.  — APPARATUS  AND  METHOD 


1.— PREPARATION   OF   THE   CELLS 

CERTAIN  precipitates  can  be  obtained  as  membranes  if  they 
are  formed  at  the  plane  of  contact  of  two  solutions,  or  of  a  so- 
lution and  a  solid.  Traube,  as  is  known,  was  the  first  to  pre- 
pare such  membranes,  and  he,  at  the  same  time,  worked  out 
the  conditions  under  which  they  can  be  formed,  conditions 
which  later  will  be  briefly  explained.  The  author  of  this  im- 
portant discovery  tested  membranes  obtained  from  different 
substances  as  to  their  permeability  to  dissolved  bodies  ;  and 
it  was  shown  that  substances  in  general  pass  less  easily  through 
such  membranes  than  through  those  formerly  employed  in  dios- 
motic  investigations.  Indeed,  many  substances  which  easily 
diosmose  through  the  latter  were  incapable  of  passing  through 
definite  precipitated  membranes. 

Traube  carried  out  diosmotic  investigations,  for  the  most 
part,  with  membranes  which  closed  one  end  of  a  glass  tube,  into 
which  the  substance  whose  diosmotic  properties  were  to  be 
tested  was  introduced.  Such  an  apparatus  is,  in  most  cases, 
easily  prepared  ;  a  small  quantity  of  one  of  the  solutions  neces- 
sary to  produce  a  precipitate  being  introduced  into  the  glass 

*  Selected  paragraphs  from  Pfeffer's  Osmotische  Untwsuchungen.  Leipsic, 
1877. 

3 


MEMOIRS    ON 

tube,  which  is  then  dipped  into  the  other  solution.  With  cor- 
rect procedure,  the  precipitate  is  formed  as  a  membrane  clos- 
ing the  tube,  at  the  surface  where  the  solutions  of  the  two 
"membrane-formers"  come  in  contact. 

Traube  worked  in  every  case  with  cells  protruding  free  into 
the  liquid.  These  are,  on  the  one  hand,  not  very  resistant ; 
and,  further,  they  continually  increase  in  size  as  long  as  an 
osmotic  current  of  water  flowing  in  produces  a  pressure  in 
the  interior  which  tends  to  distend  the  membrane.  By  this 
means  a  new  membrane  particle  is  inserted  as  soon  as  the  two 
membrane  -  formers  meet  in  the  enlarged  interstices  —  an  in- 
crease in  surface  by  intussusception  which  these  membranes 
very  beautifully  demonstrate.  But  even  if  it  were  possible  to 
overcome  these  and  other  difficulties  when  the  problem  is  to 
study  diosmotic  exchange,  yet  it  is  impossible,  in  freely  sus- 
pended cells,  to  measure  the  pressure  brought  about  by  osmotic 
action.  To  render  this  possible  the  membranes  must  be  placed 
against  a  support,  which  can  offer  resistance  to  ordinary  press- 
ure, but  which  is  relatively  easily  permeable  to  water  and  salts. 
The  plant  cells  furnish  us  with  the  model  desired  for  imitation. 
In  these  the  plasma  membrane,  which,  in  its  diosmotic  prop- 
erties, is  similar  to  the  artificially  precipitated  membranes,  is 
pressed  against  the  cell  wall. 

In  my  first  experiments,  freely  suspended  membranes  were 
allowed  to  increase  by  osmotic  pressure  until  they  finally  rested 
on  a  support  which  closed  one  end  of  a  glass  tube.  If,  finally, 
with  some  trouble,  this  was  accomplished,  other  difficulties  ap- 
peared, in  reference  to  measurement  of  pressure,  which  induced 
me  to  adop,t  another  course.  The  precipitated  membrane,  even 
under  slight  pressure,  would  be  squeezed  through  the  pores  even 
of  the  thickest  linen  and  silken  textures  —  i.  e.,  the  continually 
growing  membrane  appeared  on  the  other  side  of  the  texture, 
in  different  places,  in  the  form  of  small  sacs,  which  further  in- 
creased in  size  and  finally  burst. 

Attempts  to  use  thicker  material  as  supports,  such  as  parch- 
ment paper  or  porcelain  cells,  did  not  yield  favorable  results, 
for  reasons  which  I  shall  leave  undiscussed  here. 

I  obtained  the  first  favorable  result  by  proceeding  as  follows  : 
I  took  [unglazed]  porcelain  cells,  such  as  are  used  for  electric 
batteries,  and,  after  suitably  closing  them,  I  first  injected  them 
carefully  with  water,  and  then  placed  them  in  a  solution  of  cop- 

4 


THE    MODERN    THEORY    OF    SOLUTION 


per  sulphate,  while,  either  immediately  or  after  a  short  time,  I 
introduced  into  the  interior  a  solution  of  potassium  ferrocya- 
nide.  The  two  membrane-formers  now  penetrate  diosmotically 
the  porcelain  wall  separating  them,  and  form,  where  they  meet, 
a  precipitated  membrane  of  copper  ferrocyanide.  This  ap- 
pears, by  virtue  of  its  reddish-brown  color,  as  a  very  fine  line  in 
the  white  porcelain  which  remains  colorless  at  all  other  places, 
since  the  membrane,  once  formed,  prevents  the  substances 
which  formed  it  from  passing  through. 

These  membranes,  deposited 
in  the  interior  of  porcelain  walls, 
I  have  used,  moreover,  almost  ex- 
clusively for  preliminary  experi- 
ments, the  investigation  proper 
being  carried  out  with  mem- 
branes which  were  deposited  on 
the  inner  surface  of  porcelain 
cells.  All  the  experiments  to  be 
described  are  carried  out  with 
the  latter  kind  of  membranes,  if 
not  especially  stated  to  be  other- 
wise. To  prepare  these,  the  por- 
celain cells  were  completely  in- 
jected with,  e.g.,  a  solution  of 
copper  sulphate,  then  quickly 
rinsed  out  with  water,  and  a  solu- 
tion of  potassium  ferrocyanide 
afterwards  added.  More  minute 
details  as  to  the  preparation  of 
the  apparatus  will  be  given  later, 
after  this  general  account. 

In  Fig.  1,  the  apparatus  ready 
for  use,  with  the  manometer  (m) 
for  measuring  the  pressure,  is 
shown,  at  approximately  one-half 
the  natural  size.  The  porcelain 
cell  (z)  and  the  glass  pieces  v  and 
/,  inserted  in  position,  are  shown 
in  median  longitudinal  section.  a| 
The  porcelain  cells  which  I -used 
were,  on  an  average,  approximate- 

5 


MEMOIRS    ON 

ly  46  millimetres  high,  were  about  16  millimetres'  internal  diam- 
eter, and  the  walls  were  from  li  to  2  millimetres  thick.  The 
narrow  glass  tube  v,  called  the  connecting-piece,  was  fastened 
into  the  porcelain  cell  with  fused  sealing-wax,  and  the  closing 
piece  t  was  set  into  the  other  end  of  this  tube  in  the  same 
manner.  The  shape  and  purpose  of  this  are  shown  in  the 
figure.  The  glass  ring  r  was  necessary  only  in  experiments  at 
higher  temperature,  in  which  the  sealing-wax  softened.  The 
ring  was  then  filled  with  pitch,  which  also  held  together  firmly 
the  pieces  inserted  into  one  another. 

[Two pages  omitted.] 

All  porcelain  cells  were  treated  first  with  dilute  potassium 
hydroxide,  then  with  dilute  hydrochloric  acid  (about  3  per 
cent.),  and,  after  being  well  washed,  were  again  completely 
dried,  before  they  were  closed  as  already  described.  Substances 
which  are  soluble  in  these  reagents,  such  as  oxides  and  iron, 
which  under  certain  conditions  can  do  harm,  would  thus  be  re- 
moved. 

After  the  apparatus  was  closed,  the  precipitated  membrane 
was  formed,  either  in  the  wall  or  upon  the  surface,  according 
to  the  principle  already  indicated.  In  order  that  this  should 
be  done  successfully,  a  number  of  precautionary  measures  are 
necessary,  and  these  will  now  be  discussed.  Since  I  experi- 
mented chiefly  with  membranes  of  copper  ferrocyanide,  which 
were  deposited  upon  the  inner  surface  of  porcelain  cells,  I  will 
fix  attention  especially  upon  this  case. 

The  porcelain  cells  were  first  completely  injected  with  water 
under  the  air-pump,  and  then  placed,  for  at  least  some  hours,  in 
a  solution  containing  3  per  cent,  of  copper  sulphate,  and  the 
interior  was  also  filled  with  this  solution.  The  interior  only 
of  the  porcelain  cell  was  then  once  rinsed  out  quickly  writh 
Avater,  well  dried  as  quickly  as  possible,  by  introducing  strips 
of  filter  paper,  and  after  the  outside  had  dried  off  somewhat 
it  was  allowed  to  stand  some  time  in  the  air  until  it  just  felt 
moist.  Then  a  3-per-cent.  solution  of  potassium  ferrocyanide 
was  poured  into  the  cell,  and  this  immediately  reintroduced 
into  the  solution  of  copper  sulphate. 

After  the  cell  had  stood  for  from  twenty-four  to  forty- 
eight  hours  undisturbed,  it  was  completely  filled  with  the  solu- 
tion of  potassium  ferrocyanide,  and  closed  as  shown  in  Fig.  1. 
A  certain  excess  of  pressure  of  the  contents  of  the  cell  now 

6 


THE  MODERN  THEORY  OF  SOLUTION 

gradnally  manifested  itself,  since  the  solution  of  potassium 
ferrocyanide  had  a  greater  osmotic  pressure  than  the  solu- 
tion of  copper  sulphate.  After  another  twenty-four  to  forty- 
eight  hours  the  apparatus  was  again  opened,  and  generally  a 
solution  introduced  which  contained  3  per  cent,  of  potassium 
ferrocyanide  and  1^  per  cent,  of  potassium  nitrate  (by  weight), 
and  which  showed  an  excess  of  osmotic  pressure  of  somewhat 
more  than  three  atmospheres.  If  the  cell  should,  moreover,  he 
used  for  experiments  in  which  a  higher  pressure  was  produced, 
it  was  also  tested  at  a  higher  pressure  by  using  a  solution 
richer  in  potassium  nitrate.  In  these  test  experiments,  of 
course,  any  home-made  manometers  can  be  used. 
[Eleven  pages  omitted.] 

4. — MEASUREMENT   OF   THE    PRESSURE 

The  osmotic  pressures  were  measured  chiefly  with  air- 
manometers,  open  manometers  being  applicable  only  where 
smaller  pressures  were  involved.  The  form  of  my  air-manom- 
eter is  shown  in  Fig.  1,  in  approximately  half  its  natural  size. 
The  longer  closed  limb  is  connected  with  the  shorter  open 
limb  by  means  of  the  glass  cock  already  mentioned.  An  en- 
largement is  blown  upon  the  shorter  limb  for  the  reception 
of  mercury.  There  is  a  millimetre  scale  upon  both  limbs, 
starting  from  the  same  zero  point.  The  scale  upon  the  closed 
arm  is  200  millimetres  in  length.  This  arm  was  selected  of 
small  diameter  (in  the  three  manometers  which  I  employed 
it  was  between  1.166  and  1.198  millimetres),  so  that  the  os- 
motic pressure  can  be  established  more  quickly,  and  without 
any  considerable  amount  of  water  entering  the  apparatus. 
The  diameter  of  the  arm,  bent  twice  at  right  angles,  was 
larger  throughout,  and  was  from  7.5  to  8  millimetres  in  the 
enlarged  space. 

[One page  omitted] 

In  use,  the  space  in  the  open  arm  of  the  manometer  which 
was  not  filled  with  mercury,  was  filled  with  the  liquid  whose 
osmotic  action  was  to  be  tested.  The  cell  was  then  also 
filled  with  this,  after  the  manometer  was  attached,  as  shown 
in  Fig.  1,  and  then  the  final  closing  made  without  leaving 
any  air  in  the  apparatus,  in  the  manner  already  given,  with 
the  aid  of  a  glass  tube  drawn  out  to  a  capillary.  After  the 
capillary  point  is  melted  off,  it  is  recommended  to  produce 

7 


MEMOIRS    ON 


some  pressure  in  the  cell,  by  pushing  the  glass  tube  farther 
in,  in  order  to  lessen  the  time  required  to  reach  the  final 
pressure,  and  at  the  same  time  to  diminish  the  amount  of 
water  which  enters  the  apparatus.  The  apparatus  can  be 
opened  again  without  any  difficulty,  after  the  experiment  is 
over,  by  blowing  open  the  capillary  point  in  the  flame.  If 
the  form  of  the  glass  tube  t  allows  the  rubber  corks  to  ex- 
pand somewhat  at  their  inner  ends,  they  acquire  thus  a  con- 
siderable support.  Yet,  for  higher  pressures,  they  were  always 

secured  by  tying  them 
down  with  metal  wire 
(copper  or  silver  wire), 
as  champagne  bottles 
are  closed.  I  have  been 
able  to  close  the  appa- 
ratus easily,  so  that  it 
would  withstand,  per- 
fectly, a  pressure  of  sev- 
en atmospheres. 

The  closed  cell,  as 
seen  in  Fig.  2,  is  fast- 
ened to  a  glass  rod  pass- 
ing through  a  cork,  and 
was  introduced  into  a 
bath  in  such  a  manner 
that  the  manometer,  as 
well,  was  entirely  im- 
mersed in  the  liquid. 
The  temperature  was 
measured  by  two  accu- 
rate thermometers.  By 
covering  that  portion  of 
the  bath  not  closed  with 
corks  with  a  brass  plate, 
evaporation  of  the  liq- 
uid was  diminished  when 
the  bath  was  filled  with 
a  dilute  solution  of  a 
membrane-former.  The  apparatus  is  represented  in  the  figure 
at  approximately  one-fourth  its  natural  size.  The  baths  held 
from  2  to  2J  litres  of  liquid. 

8 


THE  MODERN  THEORY  OF  SOLUTION 

It  is  best  to  place  the  baths  in  dishes  filled  with  sand, 
in  order  that  the  manometers  may  be  easily  adjusted  with 
accuracy  to  a  vertical  position.  If  the  entire  apparatus  is 
covered  with  a  bell-jar,  and  kept  in  a  room  of  uniform  tem- 
perature, it  is  not  difficult  to  keep  the  thermometers  con- 
stant for  several  hours  to  within  less  than  TV°.  This  constancy 
of  temperature  is  of  significance,  because  the  final  condition 
of  equilibrium  between  the  osmotic  inflow  and  filtration  un- 
der pressure  is  established  very  slowly,  especially  at  low  tem- 
peratures, and  therefore,  before  the  experiment  is  completed, 
we  are  compelled  to  assure  ourselves  that  the  mercury  stands 
at  the  same  height  in  the  manometer  for  several  hours. 

In  determining  osmotic  pressures  at  higher  temperatures, 
the  entire  vessel  was  placed  in  a  heating  apparatus  which 
was  filled  with  sand  and  covered  with  a  bell-jar,  and  whose 
temperature  was  accurately  regulated.  Care  must  be  taken, 
in  passing  from  lower  to  higher  temperatures,  that  the  junc- 
tions of  the  apparatus  are  not  injured  by  the  increased  press- 
ure which  is  caused  by  the  expansion  of  liquid  and  air. 

Small  osmotic  pressures  were,  indeed,  measured  with  an 
open  manometer,  whose  longer  arm  was  made  of  a  narrow 
tube  of  approximately  0.3  millimetre  diameter,  in  order  that 
the  condition  of  equilibrium  might  be  quickly  reached.  The 
form  and  method  of  using  this  manometer  requires  no  special 
explanation.  It  should  be  observed,  in  passing,  that  the  error 
of  measurement  is,  in  any  case,  less  than  3  millimetres. 

[Thirteen  sections  omitted.] 

17. — EXPERIMENTAL    RESULTS 
NO.  VII. 

Pressures  for  Cane- Sugar  of  Different  Concentration. 

CONCENTRATION  IN  PER 

CENT.  BY  WEIGHT.  PRESSURE. 

1 535  mm. 

2 1016     " 

2.74 1518     " 

4 2082     " 

0 3075     " 

1 535     " 

Surface  of  membrane,  17.1  square  centimetres. 
9 


THE  MODERN  THEORY  OF  SOLUTION 


TABLE  12* 

EXPERIMENTS  WITH  A  ONE -PER -CENT.  SOLUTION  OF  CANE- 
SUGAR 

[Change  in  Osmotic  Pressure  ivith  Change  in    Temperature.] 

TEMPERATURE.  PRESSURE. 

J14.2°C 51.0  cm. 

a  (32.0°C 54.4    " 

6.8°  0 50.5  cm. 

13.7°  C 52.5    " 

22.0°  C 54.8    " 

15.5°  C 52.0  cm. 

36.0°  C..  .   56.7    " 


WILHELM  FRIEDRICH  PHILIPP  PFEFFER  was  born  March  9th, 
1845,  at  Grebenstein,  Cassel.  He  received  the  Degree  of  Doc- 
tor of  Philosophy  at  Gottingen  in  1865,  was  appointed  Privat- 
docent  in  Marburg  in  1871,  and  in  1873  was  elected  to  a  sub- 
ordinate professorship  in  Bonn.  He  became  professor  in  Basel 
in  1877,  and  was  called  to  Tubingen  in  1878.  He  is  at  present 
Professor  of  Botany  in  the  University  of  Leipsic.  Some  of  his 
more  important  papers,  in  addition  to  his  investigations  of  os- 
motic pressure,  are  :  Physiological  Investigations,  Leipsic,  1873 ; 
Action  of  the  Spectrum  Colors  on  the  Decomposition  of  Carbon 
Dioxide  in  Plants;  Studies  on  Symmetry  and  the  Specific 
Causes  of  Growth;  Plant  Physiology,  Vol.  I.,  1881  ;  Construc- 
tion of  a  Number  of  Pieces  of  Apparatus  for  Investigating  the 
Growth  of  Plants.  His  measurements  of  osmotic  pressure  are, 
with  perhaps  one  slight  exception,  the  only  direct  measure- 
ments which  have  been  made  up  to  the  present. 

*  Osmotische  Untersuchungen,  p.  85. 
10 


THE    ROLE    OF    OSMOTIC    PRESSURE    IN 

THE  ANALOGY  BETWEEN  SOLUTIONS 

AND  GASES 

BY 

J.  H.  VANT  HOFF 

Professor  of  Physical  Chemistry  in  the  University  of  Berlin 
(Zeitschrift  fur  Physikalische  Chemie,  I.,  481,  1887) 


CONTENTS 

PACK 

Introduction 13 

Osmotic  Pressure 13 

ttoyle's  Laic  for  Dilute  Solutions 15 

Gay-Lussac's  Law  for  Dilute  Solutions 17 

Avogadro's  Laic  for  Dilute  Solutions 21 

General  Expression  of  Above  Laws  for  Solutions  and  Gases 24 

Confirmation  of  Avogadro's  Law  as  applied  to  Solutions: 

1.  Osmotic  Pressure 25 

2.  Loitering  of  Vapor- Pressure 26 

3.  Lowering  of  Freezing -Point 29 

Application  of  Avogadro's  Law  to  Solutions 31 

Guldberg  and  Waage's  Law 31 

Deviations  from  Avogadro's  Law  in  Solutions 34 

Variations  from  Guldberg  and  Waage's  Law 34 

Determinations  of  "i  "  for  Aqueous  Solutions ; 36 

Proof  of  the  Modified  Guldberg  and  Waage  Law 37 


THE    ROLE    OF    OSMOTIC    PRESSURE    IN 
THE  ANALOGY  BETWEEN  SOLUTIONS 

AND  GASES* 

BY 

J.  H.  VAXT  HOFF 

Ix  an  investigation,  whose  essential  aim  was  a  knowledge 
of  the  laws  of  chemical  equilibrium  in  solutions,!  it  gradually 
became  apparent  that  there  is  a  deep-seated  analogy — indeed, 
almost  an  identity — between  solutions  and  gases,  so  far  as  their 
physical  relations  are  concerned  ;  provided  that  with  solutions 
we  deal  with  the  so-called  osmotic  pressure,  where  with  gases  we 
are  concerned  with  the  ordinary  elastic  pressure.  This  anal- 
ogy will  be  made  as  clear  as  possible  in  the  following  paper,  the 
physical  properties  being  considered  first : 

1. —  OSMOTIC     PRESSURE.        KIND     OF    ANALOGY    WHICH    ARISES 
THROUGH   THIS   CONCEPTION. 

In  considering  the  quantity,  with  which  we  shall  chiefly  have 
to  deal  in  what  follows,  at  first  from  the  theoretical  point  of 
view,  let  us  think  of  a  vessel,  A,  completely 
filled,  for  example,  with   an   aqueous  solution 
of  sugar,  the  vessel  being  placed  in  water,  B. 
If,  now,  the  perfectly  solid  wall  of  the  vessel 
is  permeable  to  wa'ter,  but  impermeable  to  the 
dissolved  sugar,  the  attraction  of  the  water  by 
the  solution  will,  as  is  well  known,  cause  the 
water  to  enter  A,  but  this  action   will   soon 
reach  its  limit  due  to  the  pressure  produced  by  the  water  which 
enters  (in  minimal  quantity).     Equilibrium  exists  under  these 

*Ztschr.  Phys.  Cliem..  1.,  481,  1887. 

\Etudes  de  Dynamique  Chimie,  179;  Archives  Neerlandaisex,  2O ; 
k.  Scenska  Akademiens  Handl.,  21. 

13  XS^SE  US*: 


MEMOIRS    ON 

conditions,  and  the  pressure  exerted  on  the  wall  of  the  vessel 
we  will  designate  in  the  following  pages  as  osmotic  pressure. 

It  is  evident  that  this  condition  of  equilibrium  can  be  estab- 
lished in  A  also  at  the  outset,  that  is,  without  previous  entrance 
of  water,  by  providing  the  vessel  B  with  a  piston  which  exerts 
a  pressure  equal  to  the  osmotic  pressure.    We  can  then  see  that 
by  increasing  or  diminishing  the  pressure  on 
the  piston  it  is  possible  to  produce  arbitrary 
changes  in  the  concentration  of  the  solution, 
through  movement  of  water  in  the  one  or 
the  other  direction  through  the  walls  of  the 
vessel. 

m   t''  ket  ^s  osm°tf c  pressure  be  described  from 

an  experimental  stand-point  by  one  of  Pfef- 
fer's*  experiments.  An  unglazed  porcelain  cell  was  used,  which 
was  provided  with  a  membrane  permeable  to  water,  but  not  to 
sugar.  This  was  obtained  as  follows  :  The  cell,  thoroughly 
moistened,  so  as  to  drive  out  the  air,  and  filled  with  a  solution 
of  potassium  ferrocyanicle,  was  placed  in  a  solution  of  copper 
sulphate.  The  potassium  and  copper  salts  came  in  contact, 
after  a  time,  by  diifusion,  in  the  interior  of  the  porous  wall, 
and  formed  there  a  membrane  having  the  desired  property.  Such 
a  vessel  was  then  filled  with  a  one-per-cent.  solution  of  sugar, 
and,  after  being  closed  by  a  cork  with  manometer  attached,  was 
immersed  in  water.  The  osmotic  pressure  gradually  makes  its 
appearance  through  the  entrance  of  some  water,  and  after  equi- 
librium is  established  it  is  read  on  the  manometer.  Thus,  the 
one-per-cent.  solution  of  sugar  in  question,  which  was  diluted 
only  an  insignificant  amount  by  the  water  which  entered, 
showed,  at  6.8°,  a  pressure  of  50.5  millimetres  of  mercury, 
therefore  about  T^  of  an  atmosphere. 

The  porous  membranes  here  described  will,  under  the  name 
"  semipermeable  membranes,"  find  extensive  application  in 
what  follows,  even  though  in  some  cases  the  practical  applica- 
tion is,  perhaps,  still  unrealized.  They  furnish  a  means  of 
dealing  with  solutions,  which  bears  the  closest  resemblance  to 
that  used  with  gases.  This  evidently  arises  from  the  fact  that 
the  elastic  pressure,  characteristic  of  the  latter  condition,  is 
now  introduced  also  for  solutions  as  osmotic  pressure.  At  the 

*  Osmotische  Untersuchungen,  Leipsic,  1877. 
14 


THE  MODERN  THEORY  OF  SOLUTION 

same  time  let  stress  be  laid  upon  the  fact  that  we  are  not  deal- 
ing here  with  an  artificially  forced  analogy,  but  with  one  which 
is  deeply  seated  in  the  nature  of  the  case.  The  mechanism 
by  which,  according  to  our  present  conceptions,  the  elastic 
pressure  of  gases  is  produced  is  essentially  the  same  as  that 
which  gives  rise  to  osmotic  pressure  in  solutions.  It  depends, 
in  the  first  case,  upon  the  impact  of  the  gas  molecules  against 
the  wall  of  the  vessel ;  in  the  latter,  upon  the  impact  of  tke. 
molecules  of  the  dissolved  substance  against  the  semipermeaDre 
membrane,  since  the  molecules  of  the  solvent,  being  present 
upon  both  sides  of  the  membrane  through  which  they  pass,  do 
not  enter  into  consideration. 

The  great  practical  advantage  for  the  study  of  solutions, 
which  follows  from  the  analogy  upon  which  stress  has  been 
laid,  and  which  leads  at  once  to  quantitative  results,  is  that 
the  application  of  the  second  law  of  thermodynamics  to  solu- 
tions has  now  become  extremely  easy,  since  reversible  processes, 
to  which,  as  is  well  known,  this  law  applies,  can  now  be  per- 
formed with  the  greatest  simplicity.  It  has  been  already  men- 
tioned above  that  a  cylinder,  provided  with  semipermeable 
walls  and  piston,  when  immersed  in  the  solvent,  allow  any 
desired  change  in  concentration  to  be  produced  in  the  solution 
beneath  the  piston  by  exerting  a  proper  pressure  upon  the 
piston,  just  as  a  gas  is  compressed  and  can  then  expand  ;  only 
that  in.^he  first  case  the  solvent,  in  these  changes  in  volume, 
moves  through  the  wall  of  the  cylinder.  Such  processes  can, 
in  both  cases,  preserve  the  condition  of  reversibility  with  the 
same  degree  of  ease,  provided  that  the  pressure  of  the  piston 
is  equal  to  the  counter-pressure,  i.e.,  with  solutions,  to  the 
osmotic  pressure. 

We  will  now  make  use  of  this  practical  advantage,  especially 
for  the  investigation  of  the  laws  which  hold  for  "ideal  solu- 
tions," that  is^  for  solutions  which  are  diluted  to  such  an  ex- 
tent that  they  are  comparable  with  "  ideal  gases/'  and  in  which, 
therefore,  the  reciprocal  action  of  the  dissolved  molecules  can 
be  neglected,  as  also  the  space  occupied  by  these  molecules,  in 
comparison  with  the  volume  of  the  solution  itself. 

2. — BOYLE'S  LAW  FOR  DILUTE  SOLUTIONS. 
The  analogy  between  dilute  solutions  and  gases  acquires  at 
once  a  more  quantitative  form,  if  we  consider  that  in  both 

15 


MEMOIRS    ON 

cases  the  change  in  concentration  exerts  a  similar  influence  on 
the  pressure  ;  and,  indeed,  the  values  in  question  are,  in  botli 
cases,  proportional  to  one  another. 

This  proportionality,  which  for  gases  is  designated  as  Boyle's 
law,  can  be  shown  for  osmotic  pressure,  experimentally  from 
data  already  at  hand,  and  also  theoretically. 

Experimental  Proof.     Determination  of  the  Osmotic  Pressure 

«  Different  Concentrations.  —  Let  us  first  give  the  results  of 
offer's  determinations*  of  osmotic  pressure  (P)  in  solutions 
of  sugar,  at  the  same  temperature  (13.2°-16.1°)  and  different 
concentrations  (C)  : 


\<fc  ..........   535  mm  ..........  535 

2fc  ..........  1016     "  ......  ....508 

2.74$  ..........  1518    "  ..........  554 

4$  ..........  2082     "  ..........  521 

Qfc  ..........  3075     "  ..........  513 

p 

The  nearly  constant  value  of  —  indicates  that,  in  fact,  a  pro- 

\j 

portionality  between  pressure  and  concentration  exists. 

Experimental  Proof.  Comparison  of  Osmotic  Pressure  "by 
Physiological  Methods.  —  The  observations  of  De  Vriesf  can  be 
placed  with  the  above  as  a  second  line  of  evidence.  From 
these  it  follows  that  equal  changes  in  concentration  of  solu- 
tions of  sugar,  potassium  nitrate,  and  potassium  sulphate,  ex- 
ert the  same  influence  on  the  osmotic  pressure.  The  above- 
named  investigator  compared,  by  physiological  methods,  the 
osmotic  pressure  of  these  with  that  of  the  contents  of  a  plant 
cell  whose  protoplasmic  sac  contracts  when  the  cell  is  in- 
troduced into  a  solution  which  has  stronger  attraction  for 
water.  By  a  systematic  comparison  of  different  solutions  of 
the  three  substances  named,  with  the  same  cells,  three  so- 
called  isotonic  liquids  were  obtained,  i.  e.,  solutions  of  equal 
osmotic  pressure.  Then  cells  of  another  plant  were  used, 
and  thus  four  such  isotonic  series  were  prepared,  whereby  a 
similar  relation  appeared  in  the  respective  concentrations,  as 

*  Otmotisdie  UntersucJiungen,  p.  71.     [This  volume,  p.  10.] 
\  Eine  Methode  zur  Analyse  der  Turrjorkraft,  Pringslieim's  Jahrb.,  14. 

10 


THE    MODERN    THEORY    OF    SOLUTION 

is   shown    in    the  following  table,  in  which  the  concentration 
is  expressed  in  gram-molecules*  per  litre  : 

Series  KNO3  CiaH22On  K2SO4  KNO3=1  C12H22On  R.,SO4 

I.  0.12  0.09  1  0.75 

II.  0.13  0.2  0.1  1  1.54  0.77 

III.  0.195         0.3  0.15  1  1.54  0.77 

IV.  0.26  0.4  1  1.54 

Theoretical  Demonstration. — Although  the  observations  men- 
tioned make  it  very  probable  that  there  is  a  proportionality 
between  osmotic  pressure  and  concentration,  yet  the  theoret- 
ical demonstration  is  a  welcome  supplement,  especially  since 
it  is  almost  self-evident.  If  we  regard  osmotic  pressure  as  of 
kinetic  origin,  therefore  as  being  produced  by  the  impacts  of 
the  molecules  of  the  dissolved  substance,  the  demonstration 
depends  upon  the  proportionality  between  the  number  of  im- 
pacts in  unit  time  and  the  number  of  molecules  in  unit  space. 
The  demonstration  is,  then,  exactly  the  same  as  that  for  Boyle's 
law  with  ideal  gases.  If,  on  the  other  hand,  we  regard  osmotic 
pressure  as  the  expression  of  an  attraction  for  water,  the  value 
of  this  is  evidently  proportional  to  the  number  of  attracting 
molecules  in  uui-t  volume,  provided  the  dissolved  molecules 
have  no  action  upon  one  another,  and  each  exerts,  therefore, 
its  own  special  attraction,  as  can  be  assumed  with  sufficiently 

dilute  solutions. 

~Hh 

'  ^_ 

3,— GAY-LUSSAC'S   LAW   FOR    DILUTE   SOLUTIONS. 

While  the  proportionality  between  concentration  and  osmot- 
ic pressure  at  constant  temperature  is  self-evident,  it  is  dif- 
ferent with  the  proportionality  between  osmotic  pressure  and 
absolute  temperature  at  constant  concentration.  Neverthe- 
less, this  proposition  can  be  demonstrated  on  thermodynamic 
grounds,  and  experimental  data  can  also  be  cited  which  are 
very  favorable  to  the  results  obtained  thermodynamically. 

Theoretical  Demonstration. — It  has  already  been  mentioned 
that  reversible  transformations  can  be  carried  out  by  means  of 

*  [A  gram-molecule  of  a  substance  is  the  molecular  weight  of  the  substance 
in  grams,  e.g.  58.5  grams  of  sodium  chloride.} 
B  17 


MEMOIRS    ON 

a  piston  and  cylinder  with  semipermeable  walls,  which  we  will 
now  use  to  complete  a  cycle.  If  we  express  this  in  the  way 
which  is  well  known  for  gases,  volume  and  pressure  are  rep- 
resented on  the  axes  0V  and  OP,  only  that  we  must  again 
deal  here  with  the  osmotic  pressure.  Let 
the  originaLxohime  (  FJf/-8)*  be  repre- 
sented by  OAj  the  original  pressure  on 
the  piston  (PK°),  which  is  1  Mr'  ',  by  Aq, 
the  absolute  temperature  by  T;  now  let 
the  solution  undergo  a  minimum  increase 
in  volume  of  dVMr3  (  =  AB)  by  moving 
A  DEC  v  the  piston  a  distance  d  VMr,  while  the 
Fig.  3.  temperature  of  the  solution  is  main- 

tained constant  by  adding  the  requisite 

amount  of  heat.  But  this  amount  of  heat  can  be  determined 
at  once,  since  it  just  serves  to  perform  the  known  external 
work  PdV,  by  moving  the  piston.  No  internal  work  is  done, 
since  we  are  dealing  with  a  dilution  which  is  so  great  that  the 
dissolved  molecules  have  no  action  upon  one  another.  This 
isothermal  change  ab  is  followed  by  the  so-called  isen  tropic 
change  be,  during  which  heat  is  neither  given  out  nor  absorbed. 
The  temperature  falls,  then,  dT,  after  which  return  to  the  orig- 
inal condition  follows  through  a  second  isothermal  and  a  sec- 
ond isentropic  transformation,  cd  and  da,  respectively.  As  is 
known,  the  se^on.d  law  of  thermodynamics  requires  that  a 
fraction  of  the  amount  of  heat  PdV,  imparted  at  the  begin- 

dT 
ning,  equal  to  -^PdV,  is  converted  into  work.      This  must, 

therefore,  be  equivalent  to  the  area  of  the  quadrilateral  abed  ; 
from  which  we  obtain  the  following  equation  : 


dT 
therefore  :  ^~r  ~af' 

But  af,  in  the  above,  is  the  change  of  the  osmotic  pressure  at 
constant  volume,  resulting  from  a  change  in  temperature  dT. 

i.  e.,  I  —=A  dT\  from  which,  finally,  we  have  : 

\Cl  1  /v 

*  [Mr  is  metre.    K  is  kilogram.] 
18 


THE    MODERN    THEORY    OF    SOLUTION 


\dTfr 


Tliis  equation  gives,  however,  on  integration,  keeping  vol- 
ume constant  :  p 

—,  =  constant. 

That  is  to  say,  the  osmotic  pressure  is  proportional  to  the 
absolute  temperature,  in  case  volume  or  concentration  remains 
the  same,  which  proposition  for  solutions  is  perfectly  analo- 
gous to  the  law  of  Gay-Lussac  for  gases. 

Experimental  Proof.  Determination  of  the  Osmotic  Pressure 
at  Different  Temperatures. — Let  us  next  compare  the  theoretical 
conclusion  just  reached  with  the  results  of  Pfeffer's  investiga- 
tions.* This  investigator  found,  as  a  matter  of  fact,  that  the 
osmotic  pressure,  without  exception,  increases  with  rise  in 
temperature.  We  will,  moreover,  see  that  although  the  experi- 
mental results  referred  to  do  not  suffice  to  make  the  above 
proposition  absolutely  certain,  yet  an  excellent  approximation 
between  observation  and  calculation  often  appears.  If  from 
one  of  two  experiments  carried  out  with  the  same  solution  at 
different  temperatures  we  calculate  the  result  of  the  other,  on 
the  assumption  of  Gay-Lussac's  law,  and  compare  it  with  the 
value  directly  obtained,  we  have  : 

1.  Solution  of  cane-sugar. 

At  32°  a  pressure  of  544  millimetres  was  observed. 
At  14°. 15  the  calculated  pressure  is  512  millimetres,  in- 
stead of  510  millimetres  observed. 

2.  Solution  of  cane-sugar. 

At  36°  the  pressure  observed  was  567  millimetres. 
At  15°. 5  the  calculated  pressure  is  529  millimetres,  instead 
of  520.5  millimetres  observed. 

3.  Solution  of  sodium  tartrate. 

At  36°.  6  the  pressure  observed  was  15G4  millimetres. 
At  13°. 3  the  calculated  pressure  is  1443  millimetres,  instead 
of  1431.6  millimetres  found. 

4.  Solution  of  sodium  tartrate. 

At  3 7°. 3  the  pressure  observed  was  983  millimetres. 
At  13°.3  the  calculated  pressure  is  907  millimetres,  instead 
of  908  millimetres  found. 

*  Osmotisclie  UntersncJiurirjcn,  pp.  114,  115.     [77m  volume,  p.  10.] 

19 


MEMOIRS    ON 

Experimental  Proof.  Comparison  of  Osmotic  Pressure  by 
Physiological  Methods. — Just  as  the  law  of  Boyle,  applied  to  so- 
lutions, received  support  from  the  fact  that  isotonic  solutions 
of  different  substances  preserve  equality  of  osmotic  pressure 
when  the  respective  concentrations  were  reduced  to  the  same 
fraction,  so  the  law  of  Gay-Lussac  is  supported  by  the  result 
that  this  isotonism  is  likewise  preserved  for  equal  change  in 
temperature.  This  fact  was  also  established  by  physiological 
methods,  this  time  by  Bonders  and  Hamburger,*  who,  working 
in  a  manner  similar  to  that  of  De  Vries,  but  now  with  animal 
cells  ( blood  corpuscles ),  found  that  solutions  of  potassium 
nitrate,  sodium  chloride,  and  sugar,  which  are  isotonic  with  the 
contents  of  the  cells  in  question,  at  0°,  and,  therefore,  with  one 
another,  show  exactly  the  same  relation  at  34°,  as  will  be  seen 
from  the  following  table  : 

TEMPERATURE  0°.  TEMPERATURE  34°. 

KN03 1.052-1.03  % 1.052-1.03  $ 

NaCI 0.62  -0.609$ 0.62  -0.609$ 

C]2H22On 5.48  -5.38$ 5.48  -5.38$ 

Experimental  Proof  of  the  Laws  of  Boyle  and  Gay-Lussac 
for  Solutions.  Experiments  of  Soret.\ — The  phenomenon  ob- 
served by  Soret  is  very  significant  for  the  analogy  between 
gases  and  solutions,  where  we  are  dealing  with  the  influ- 
ence of  concentration  and  temperature  on  the  pressure  and 
on  osmotic  pressure  respectively.  It  became  apparent  from 
these  experiments  that,  just  as  with  a  difference  in  tempera- 
ture in  gases,  the  warmest  part  is  the  most  dilute,  so,  also, 
with  solutions  the  same  relation  obtains  ;  only  that  in  the  lat- 
ter case  the  time  required  to  establish  the  final  condition  of 
equilibrium  is  considerably  greater.  The  experiments  were 
made  in  vertical  tubes,  in  such  a  manner  that  the  upper  por- 
tion of  the  solution  contained  in  them,  which  was  perfectly 
homogeneous  at  the  beginning,  was  warmed  at  a  constant  tem- 
perature, while  the  under  portion  was  likewise  cooled  to  a  def- 
inite temperature. 

*  Onderzoekingen  gedaan  in  het  pJiysiologisch.  Labor  atorium  der  Utreclit- 
sche  Hoogeschool,  (3),  9,  26. 

f  Archives  des  Sciences  phys.  et  nat.,  (3),  2,  48;  Ann.  Chim.  P/<yx.. 
(5),  22,  293. 

20 


THE  MODERN  THEORY  OF  SOLUTION 

If,  then,  the  observation  of  Soret  contains,  qualitatively,  a 
complete  confirmation  of  the  laws  developed,  so,  also,  a  wel- 
come approximation  to  our  theory  is  to  be  found  in  his  quanti- 
tative results,  at  least  in  the  latest  experiments.  It  would  be 
expected,  as  with  gases,  that  equilibrium  exists  when  the  iso- 
tonic  state  is  reached;  and  where  the  osmotic  pressure  increases 
proportional  to  the  concentration  and  to  the  absolute  tempera- 
ture, this  isotonic  state  of  the  parts  of  the  solution  will  occur 
when  the  products  of  the  two  values  are  equal. 

If,  on  this  basis,  we  calculate  the  concentration  of  the 
warmer  part  of  the  solution  from  that  which  was  found  in  the 
colder  part,  and  compare  with  this  the  value  obtained  directly 
by  experiment,  we  have  : 

1.  Solution  of  copper  sulphate. 

The  part  cooled  to  20°  contained  17.332  per  cent.  14.3 
per  cent,  would  correspond  to  a  temperature  of  80°;  in- 
stead of  this,  14.03  per  cent,  was  found. 

2.  Solution  of  copper  sulphate. 

The  part  cooled  to  20°  contained  29.867  per  cent.  24.8 
per  cent,  would  correspond  to  a  temperature  of  80°;  in- 
stead of  this,  23.871  per  cent,  was  found. 

It  must,  indeed,  be  added  that  the  earlier  experiments  of 
Soret  gave  less  favorable  results,  yet,  on  account  of  the  diffi- 
culty of  such  observations,  too  much  stress  must  not  be  laid 
upon  them. 

4. — AVOGADRO'S   LAW   FOR   DILUTE   SOLUTIONS. 

While  up  to  the  present  essentially  only  those  changes  have 
been  dealt  with  which  the  osmotic  pressure  in  solutions  under- 
goes due  to  changes  in  concentration  and  temperature,  and 
while  the  agreement  with  the  corresponding  laws  which  hold 
for  gases  manifested  itself,  we  must  now  deal  with  the  direct 
comparison  of  the  two  analogous  quantities,  elastic  pressure  and 
osmotic  pressure  of  one  and  the  same  substance.  It  is  evident 
that  this  applies  to  gases  which  have  also  been  investigated  in 
solution  ;  and,  as  a  matter  of  fact,  it  will  be  proved  that,  in 
case  the  law  of  Henry  is  satisfied,  the  osmotic  pressure  in  solu- 
tion is  exactly  equal  to  the  elastic  pressure  as  gas,  at  least  at 
the  same  temperature  and  concentration. 

21 


MEMOIRS    ON 


For  the  purpose  of  demonstration,  we  will  perform  a  reversi- 
ble cycle  at  constant  temperature,  by  means  of  semipermeable 
walls,  and  then  employ  the  second  law  of  thermodynamics, 
which,  in  this  case,  as  is  known,  leads  to  an  extremely  simple 
result,  that  no  heat  is  transformed  into  work,  or  work  into  heat, 
and  consequently  the  sum  of  all  the  work  done  must  be  equal 
to  zero. 

The  reversible  cycle  is  performed  by  two  similarly  arranged 
double  cylinders,  with  pistons,  like  one  already  described.  One 

cylinder  is  partly  filled  with  a  gas 
(A),  say  oxygen,  in  contact  with  a  so- 
lution  of  oxygen  (5),  saturated  under 
the  conditions  of  the  experiment ;  for 
example,  an  aqueous  solution.  The 
wall  be  allows  only  oxygen  but  no 

water  to  pass  through; the  wal1  ab> 

on  the  contrary,  allows  water  but  not 
oxygen  to  pass,  and  is  in  contact  on 
the  outside  with  the  liquid  (E)  in 
question.  A  reversible  transformation  can  be  made  with  such 
a  cylinder;  which  amounts  to  this,  that  by  raising  the  two 
pistons  (1)  and  (2)  oxygen  is  evolved  from  its  aqueous  solution 
as  gas,  while  water  is  removed  through  ab.  This  transformation 
can  take  place  so  that  the  concentrations  of  gas  and  solution 
remain  the  same.  The  only  difference  between  the  two  cyl- 
inders is  in  the  concentrations  which  are  present  in  them. 
These  we  will  express  in  the  following  manner: 

The  unit  of  weight  of  the  substance  in  question  fills,  in  the 
left  vessel,  as  gas  and  as  solution,  the  volumes  v  and  V  respec- 
tively, in  the  right  of  v  +  dv  and  V+dV\  then,  in  order  that 
Henry's  law  be  satisfied,  the  following  relation  must  obtain  : 

v:V=(v  +  dv)  '.(V+dV) 
therefore  :  v  :  V—  dv  :  d  V. 

Let  now  the  pressure  and  osmotic  pressure  of  gas  and  solu- 
tion, in  case  unit  weight  is  present  in  unit  volume,  be  respec- 
tively P  and  p  (values  which  hereafter  will  be  shown  to  be 
equal),  the  pressure  in  gas  and  solution  is,  then,  from  Boyle's 

P  i} 

law,  respectively,  --  and  ~. 

If  we  now  raise  the  pistons  (1)  and  (2),  and  thus  liberate  a 
unit  weight  of  the  gas  from  the  solution,  we  increase,  then, 

22 


THE  MODERN  THEORY  OF  SOLUTION 

x  ^vvafcvA" 

this  gas  volume  v  by  dv,  in  order  that  it  may  have  the  concen- 
tration of  the  gas  in  the  left  vessel  ;  if  the  gas  just  set  free  is 
forced  into  solution  by  lowering  pistons  (4)  and  (5),  and  thus 
the  volume  of  the  solution  F-frfFdiminished  by  d  Fin  the  cyl- 
inder with  setnipermeable  walls,  the  cycle  is  then  completed. 

Six  amounts  of  work  are  to  be  taken  into  consideration, 
whose  sum,  from  what  is  stated  above,  must  be  equal  to  zero. 
We  will  designate  these  by  numbers,  whose  meaning  is  self- 
evident.  We  have,  then  : 

(1)4-  (2)  -f  (3)  +  (4)  +  (5)  +  (6)  =  0. 

But  (2)  and  (4)  are  of  equal  value  and  opposite  sign,  since 
we  are  dealing  with  volume  changes  v  and  v  +  dv,  in  the  op- 
posite sense,  which  take  place  at  pressures  which  are  inversely 
proportional  to  the  volumes.  For  the  same  reasons  the  sum 
of  (1)  and  (5)  is  zero  ;  then,  from  the  above  relation  : 


The  work  done  by  the  gas  (3),  in  case  it  undergoes  an  in- 

p 
crease  in  volume  dv  at  a  pressure  —  ,  is  : 


while  the  work  done  by  the  solution  (6),  in  case  it  undergoes  a 
diminution  in  volume  dV  at  an  osmotic  pressure      ,  is  : 


(G)=  - 


We  obtain,  then  : 


.and  since  v  :  V—dv  :dV,  P  and  p  must  be  equal,  which  was  to 
be  proved. 

The  conclusion  here  reached,  which  will  be  repeatedly  con- 
firmed in  what  follows,  is,  in  turn,  a  new  support  to  the  law 
of  Gay-Lussac  applied  to  solutions.  In  case  gaseous  pressure 
and  osmotic  pressure  are  equal  at  the  same  temperature, 
changes  in  temperature  must  have  also  an  equal  influence  on 
both.  But,  on  the  other  hand,  the  relation  found  permits  of 
an  important  extension  of  the  law  of  Avogadro,  which  now 
finds  application  also  to  all  solutions,  if  only  osmotic  pressure 
is  considered  instead  of  elastic  pressure.  At  equal  osmotic 
pressure  and  equal  temperature,  equal  volumes  of  the  most 

23 


MEMOIRS    ON 

widely  different  solutions  contain  an  equal  number  of  mole- 
cules, and,  indeed,  the  same  number  which,  at  the  same  press- 
ure and  temperature,  is  contained  in  an  equal  volume  of  a  gas. 

5.  —  GENERAL     EXPRESSION     OF     THE     LAWS     OF     BOYLE,    GAY- 
LUSSAC,  AND   AVOGADRO,  FOR   SOLUTIONS   AND   GASES. 

The  well-known  formula,  which  expresses  for  gases  the  two 
laws  of  Boyle  and  Gay-Lussac  : 

PV=RT, 

is  now,  where  the  laws  referred  to  are  also  applicable  to  liquids, 
valid  also  for  solutions,  if  we  are  dealing  with  the  osmotic  pres- 
sure. This  holds  even  with  the  same  limitation  which  is  also 
to  be  considered  with  gases,  that  the  dilution  shall  be  sufficiently 
great  to  allow  one  to  disregard  the  reciprocal  action  of,  and  the 
space  taken  by,  the  dissolved  particles. 

If  we  wish  to  include  in  the  above  expression,  also,  the  third, 
the  law  of  Avogadro,  this  can  be  done  in  an  exceedingly  simple 
manner,  following  the  suggestion  of  Horstmann,*  considering 
always  kilogram-molecules  of  the  substance  in  question;  thus, 
2  k.  hydrogen,  44  k.  carbon  dioxide,  etc.  Then  R  in  the 
above  equation  has  the  same  value  for  all  gases,  since  at  the 
same  temperature  and  pressure  the  quantities  mentioned  oc- 
cupy also  the  same  volume.  If  this  value  is  calculated,  and 
the  volume  taken  in  Mr*,  the  pressure  in  K°  per  Mr*,  and 
if,  for  example,  hydrogen  at  0°  and  atmospheric  pressure  is 
chosen  : 

"P  =  10333,  F  =         --,  ^3,^  =  845.05.  . 


The  combined  expression  of  the  laws  of  Boyle,  Gay-Lussac, 
and  Avogadro  is,  then  : 

PF=845  T, 

and  in  this  form  it  refers  not  only  to  gases,  but  to  all  solutions, 
P  being  then  always  taken  as  osmotic  pressure. 

In  order  that  the  formula  last  obtained  may  be  hereafter  easily 
applied,  we  give  it  finally  a  simpler  form,  by  observing  that  the 
number  of  calories,  which  is  equal  to  a  kilogram-metre,  there- 


fore to  the   equivalent   of   work f  [A  =— —  V  stands  i 

\         4/w/ 


in  a  very 


*  Ber.  deutscli.  chem.  GeselL,  14,  1243. 
f  [The  reciprocal  of  the  "mechanical  equivalent  of  heat.''1'] 
24 

-      -   /  f\  1-JsA^A-      f^-*    °y-\  »,>/**••». 

'  i~*     ,->  <* 

v    •*' 


THE    MODERN    THEORY    OF    SOLUTION 

simple  relation  to  R,  indeed,  AR—^,  (more  exactly,  about  one- 
thousandth  less). 

Therefore,  the  following  form  can  be  chosen  : 

APV=2  T, 

which  has  the  great  practical  advantage  that  the  work  done, 
of  which  we  shall  often  speak  hereafter,  finds  a  very  simple  ex- 
pression, in  case  it  is  calculated  in  calories. 

Let  us  next  calculate  the  work,  expressed  in  calories,  which 
is  done  when  a  gas  or  a  solution  at  constant  pressure  and  tem- 
perature expands  by  a  volume  V,  a  kilogram -molecule  being 
the  mass  involved.  This  work  is  evidently  2  T.  We  should 
add  that  this  constant  pressure  is  preserved  only  if  the  entire 
volume  of  gas  or  solution  is  very  large  in  proportion  to  V,  or 
if  we  are  dealing  with  vaporization  at  maximum  tension. 

The  subordinate  question  will  often  arise,  of  the  work  ex- 
pressed in  calories,  which  is  done  by  isothermal  expansion, 
either  by  a  kilogram-molecule  of  a  gas,  or,  if  it  is  a  solution,  by 
that  amount  which  contains  this  quantity  of  the  dissolved 
substance.  If  the  pressure  decreases,  then,  by  a  very  small 
fraction  AP,  which  therefore  corresponds  to  an  increase  in  vol- 
ume of  A  V,  the  work  done  will  be  AP&  V,  or  2  A7T. 


0. — FIRST   CONFIRMATION    OF  AYOGADRO'S  LAW  AS  APPLIED  TO 
SOLUTIONS.     DIRECT   DETERMINATION  OF  OSMOTIC  PRESSURE. 

It  would  be  expected  beforehand  that  the  law  of  Avogadro, 
which  we  developed  for  solutions  of  gases,  as  a  consequence  of 
the  law  of  Henry,  would  not  be  limited  to  solutions  of  those 
substances  which,  perchance,  are  in  the  gaseous  state  under 
ordinary  conditions.  Yet  the  confirmation  of  this  conjecture 
is  very  welcome  in  other  cases,  especially  in  those  now  to  be 
mentioned,  since  we  are  not  dealing  here  with  theoretical  con- 
clusions, but  with  the  results  of  direct  experiment.  As  a  mat- 
ter of  fact,  we  will  find  in  Pfeffer's  determinations  of  the  os- 
motic pressure  of  solutions  of  sugar*  a  striking  confirmation 
of  the  law  which  we  are  defending. 

A  one-per-cent.  solution  of  sugar  was  used  in  the  experi- 
ment under  consideration,  i.e.,  a  solution  obtained  by  bringing 


*  Osmotische  UntersucJiungen,  Leipsic,  1877. 
25 


MEMOIRS    ON 

together  1  part  of  sugar  and  100  parts  of  water,  which  contain- 
ed, then,  1  gram  of  the  substance  named,  in  100.6  cm.3  of  the 
solution.  If  we  compare  the  osmotic  pressure  of  this  solution 
with  the  pressure  of  a  gas — say  hydrogen — which  contains  the 

same  number  of  molecules  in  100.6  cm.3,  therefore,  in  the  case 

2 

chosen,—-  grams  (C12H22011  =  342),  a  striking  agreement  be- 
comes manifest.  Since  hydrogen  at  one  atmosphere  pressure 
and  at  0°  weighs  0.08956  grams  per  litre,  and  the  above  con- 
centration contains  0.0581  grams  per  litre,  we  are  dealing, 
ut  0°,  with  0.649  atmosphere,  and,  therefore,  at  /°,  with  0.641) 
(1  +  0.003670-  If  we  compare  these  with  Pfeffer's  data,  we 
have  : 

TEMPERATURE  (t).         OSMOTIC   PRESSURE.  0.649(1+0.00867$). 

6.8 0.664.. 0.665 

13.7 0.691 0.681 

14.2 0.671 0.682 

15.5 0.684 0.686 

22.0 0.721 0.701 

32.0 0.716 0.725 

36.0 0.746 0.735 

The  osmotic  pressure  of  a  solution  of  sugar,  ascertained  di- 
rectly, is,  then,  at  the  same  temperature,  exactly  equal  to  the 
gas  pressure  of  a  gas  which  contains  the  same  number  of  mole- 
cules in  a  given  volume  as  there  are  sugar  molecules  in  the 
same  volume  of  the  solution. 

This  relation  can  be  extended  from  cane-sugar  to  other  dis- 
solved substances;  as  invert  sugar,  malic  acid,  tartaric  acid,  cit- 
ric acid,  malate  and  sulphate  of  magnesium,  which,  from  the 
physiological  investigations*  of  De  Vries,  show  the  same  osmot- 
ic pressure  for  equal  molecular  concentration  of  the  solutions. 

7.— SECOND  CONFIRMATION  OF  THE  LAW  OF  AVOftADRO  AS 
APPLIED  TO  SOLUTIONS.  MOLECULAR  LOWERING  OF  VAPOR- 
PRESSURE. 

The  relation  which  exists  between  osmotic  pressure  and 
maximum  vapor-tension,  and  which  can  be  easily  developed  on 

*  Eine  Methode  zur  Messung  der  Turgorkraft,  512. 
26 


THE  MODERN  THEORY  OF  SOLUTION 

thermodynamic  gronnds,  furnishes  a  suitable  means  of  testing 
the  laws  in  question,  through  the  experimental  material  re- 
cently collected  by  Raoult. 

\Ve  shall  then  begin  with  a  perfectly  general  law,  which  is 
rentirely  independent  of  that  hitherto  developed  :  Isotonism  in 
\xolutiom  in  the  same  solvent  Conditions  equality  of  maximum 
I  tension.  This  proposition  can  be  easily  demonstrated  by  car- 
rying out  a  reversible  cycle  at  constant  temperature.  For  this 
purpose  two  solutions  are  taken  with  the  same  maximum  ten- 
sion, and  a  small  amount  of  the  solvent  is  transported,  in  a  re- 
versible manner,  from  one  to  the  other,  as  vapor,  i.  e.,  with  pis- 
ton and  cylinder.  This  transference  takes  place  when  the 
maximum  tensions  are  equal,  without  doing  work,  therefore  no 
work  is  done  in  returning  the  solvent,  since  in  the  whole  cycle 
no  work  can  be  done.  If  we  now  return  the  solvent  by  means 
of  a  semipermeable  wall,  which  separates  the  two  solutions,  the 
necessity  of  the  isotonic  state  is  at  once  evident,  since  otherwise 
this  transformation  could  not  take  place  without  doing  work. 

If  we  apply  this  principle  to  dilute  solutions,  with  the  aid  of 
the  laws  developed  for  them,  we  arrive  at  once  at  the  simple 
conclusion  that  equal  molecular  concentration  of  dissolved 
substance  conditions  equal  maximum  tension  of  the  solution. 
But  this  is  exactly  the  principle  recently  discovered  by  Raoult,* 
of  the  constancy  of  molecular  lowering  of  vapor  -  pressure. 
This  is,  however,  obtained  by  multiplying  the  molecular  weight 
of  dissolved  substances  with  the  so-called  relative  lowering  of 
the  vapor-pressure  of  a  one-per-cent.  solution,  i.  e.,  with  the 
part  of  the  maximum  tension  which  the  solvent  has  thus  lost. 
The  equality  of  the  molecular  lowering  of  vapor-pressure  refers 
then  to  solutions  of  equi-molecular  concentration,  on  the  as- 
sumption of  the  approximate  proportionality  between  lowering 
of  vapor-pressure  and  concentration.  For  example,  the  value 
in  question  for  ether,  for  the  thirteen  substances  which  were 
investigated  in  it,  fluctuated  between  0.07  and  0.74,  with  a 
mean  of  0.71. 

But  we  can  carry  this  relation  still  further,  and  com- 
pare the  different  solvents  with  one  another,  to  arrive  at  the 
second  law  which  Raoult  likewise  found  experimentally. 
For  this  purpose,  we  perform,  at  T°,  with  a  very  dilute 

*  Camp,  rend.,  87,  167;  44,  1431. 

27 


MEMOIRS    ON 

P-per-cent.  solution,  the  following  reversible  cycle,  consisting 
of  two  parts  : 

1.  That  mass  of  the  solvent  is  removed  by  means  of  piston 
and  cylinder  in  which  a  kilogram-molecule  ( M )  of  the  dissolved 
substance  is  contained.     The  mass  of  the  solution  is  so  large 
that  change  in  concentration  is  not  thus  produced,  and  the 
work  done  amounts,  therefore,  to  2  T. 

2.  The  amount  of  solvent  just  obtained,  — 73 —  kilograms,  is 

returned  as  vapor  in  a  reversible  way,  therefore  first  obtained 
from  the  liquid  at  maximum  tension,  then  expanded  until  the 
maximum  tension  of  the  solution  is  reached,  and  finally  lique- 
fied in  contact  with  the  solution.  The  kilogram-molecule  of 
the  solvent  (M')  would  require,  thus,  an  expenditure  of  2  A2T 
work,  in  which  A  represents  the  relative  lowering  of  vapor- 
pressure  ;  and  therefore  the kilograms  in  question  would 

require  2  JA •     But  — Mis  Raoult's  molecular  lowering  of 

PM  P 

vapor-pressure,  which  we  will  therefore  represent  by  the  letter 
K,  whence  the  expression  in  question  becomes  simplified  to 

aoo  TK 

M' 

But  from  the  second  law  of  thermodynamics,  the  sum  of  the 
work  done  in  this  cycle,  completed  at  constant  temperature, 
must  again  be  equal  to  zero,  therefore  what  is  gained  in  the 
first  part  is  expended  in  the  second.  We  have,  consequently : 

^00  TJ? 
2  T=     M       or  100  K=M'. 

This  relation  comprises  all  of  Raoult's  results.  It  expresses, 
at  once,  what  was  obtained  above,  that  the  molecular  lowering 
of  the  vapor-pressure  is  independent  of  the  nature  of  the  dis- 
solved substance.  But  it  shows,  also,  what  Raoult  found,  that 
the  value  in  question  does  not  change  with  the  temperature. 
It  contains,  finally,  the  second  proposition  of  Raoult,  that  the 
molecular  lowering  of  the  vapor-pressure  is  proportional  to  the 
molecular  weight  of  the  solvent,  and  amounts  to  about  one  one- 
hundredth  of  it.  The  following  figures,  obtained  by  Raoult, 
suffice  to  show  this  : 

28 


THE    MODERN    THEORY    OF    SOLUTION 

MOI  Frm  AR  WFTOHT      MOLECULAR  LOWERING 

SOLVENT.  OF  VAPOR-PRESSURE 

(K). 

.       Water 18     0.185 

Phosphorus  trichloride.  .137.5 1.49 

Carbon  bisulphide 76    0.80 

Carbon  tetrachloride 154     1.62 

Chloroform 119.5 1.30 

Amylene 70     0.74 

Benzene 78     0.83 

Methyl  iodide 142     1.49 

Methyl  bromide 109     1.18 

Ether 74    0.71 

Acetone 58     0.59 

Methyl  alcohol 32     0.33 

8.— THIRD  CONFIRMATION  OF  AVOGADRO's  LAW  AS  APPLIED 
TO  SOLUTIONS.  MOLECULAR  LOWERING  OF  THE  FREEZING- 
POINT. 

There  can  also  be  stated  here  a  perfectly  general  and  rigid 
proposition,  which  connects  the  osmotic  pressure  of  a  solution 
with  its  freezing-point.  Solutions  in  the  same  solvent,  having 
the  same  freezing-point,  are  isotonic  at  that  temperature.  This 
proposition  can  be  proved  exactly  as  the  preceding  one,  by  car- 
rying out  a  cycle  at  the  freezing-point  of  the  two  solutions  ; 
only  here  the  reversible  transference  of  the  solvent  is  effected 
not  as  vapor,  but  as  ice.  It  is  returned  again  through  a  semi- 
permeable  wall,  and  since  there  can  be  no  work  done,  isoto- 
nism  must  exist. 

We  also  apply  this  proposition  to  dilute  solutions,  and  if  we 
take  into  account,  then,  the  relations  already  developed,  we  ar- 
rive at  once  at  the  very  simple  conclusion  that  solutions  which 
contain  the  same  number  of  molecules  in  the  same  volume,  and, 
therefore,  from  Avogadro's  law,  are  isotonic,  have  also  the  same 
freezing-point.  This  was,  in  fact,  discovered  by  Raoult,  and 
found  its  expression  in  the  term  introduced  by  him,  the  so- 
called  "normal  molecular  lowering  of  the  freezing-point," 
which  is  shown  by  the  large  majority  of  dissolved  substances, 
and  means  that  the  freezing-point  lowering  of  a  one-per-cent. 
solution,  multiplied  by  the  molecular  weight,  is  constant.  This 
refers,  therefore,  to  solutions  of  equal  molecular  concentration, 

29 


MEMOIRS    ON 

on  the  assumption  of  an  approximate  proportionality  between 
concentration  and  lowering  of  freezing-point.  For  example, 
this  value  is  about  18.5  for  almost  all  organic  substances  dis- 
solved in  water. 

We  can,  however,  carry  the  relation  still  further,  and  derive 
the  above  normal  molecular  lowering  of  the  freezing-point  from 
other  data,  on  the  assumption  of  Avogadro's  law  for  solutions. 
This  quantity  bears  a  necessary  and  simple  relation  to  the  la- 
tent heat  of  fusion  of  the  solvent,  as  the  following  reversible 
cycle  shows,  using  the  second  law  of  thermodynamics.  Let  us 
take  a  very  dilute  .P-per-cent.  solution,  which  gives  a  freezing- 
point  lowering  A  ;  the  solvent  freezes  at  T,  and  its  latent  heat 
of  fusion  is  W  per  kilogram. 

1.  The  solution  is  deprived  at  T,  of  that  amount  of  the  sol- 
vent in  which  a  kilogram-molecule  (M)  of  the  dissolved  sub- 
stance is  present,  exactly  as  in  the  preceding  case,  by  means  of 
piston  arid  cylinder  with  semipermeable  wall.      The  amount  of 
the  solution  is  here  so  large  that  change  in  concentration  is  not 
thus  produced,  and  therefore  the  work  done  is  2  T. 

2.  The  kilograms  of  the  solvent  obtained,  is  allowed  to 

freeze  at  T,  when  --  -^  —  calories  are  set  free.     The  solution 

and  solid  solvent  are  cooled  A  degrees,  and  the  latter  allowed 
to  melt  in  contact  with  the  solution,  thereby  taking  up  the  heat 
just  set  free.  Finally,  the  temperature  is  again  raised  A  degrees. 

In  this  reversible  cycle  --  ^  —  calories  are  raised  from  T7—  A 
to  T,  which  corresponds  to  an  amount  of  work  ---  --  —  ,  but 

—  p-  is  the  molecular  lowering  of  the  freezing-point,  which  we 
will  designate  by  the  letter  /  ;  the  work  done  is,  therefore, 

1  00  W/ 

—  -™  —  ,  and  this  was  shown  in  the  first  part  of  the  above  process 
to  be  2  T-,  therefore  : 


or 


THE    MODERN    THEORY    OF    SOLUTION 

The  relation  thus  obtained  is  very  satisfactorily  confirmed  by 
the  facts.  We  give  the  values  calculated  from  the  formula  de- 
veloped, together  with  the  molecular  freezing-point  lowerings 
obtained  by  Raoult,*  so  that  the  two  may  be  examined. 


SOLVENT. 

Water 

FREEZING-           1 
POINT  (T).          C 

273 

LATENT  HEAT 
)F  FUSION  (W). 

79 

.     0.02  '/'     3 
W 

18.9 

1OLKCUI.AR 
LOWERING. 

18.5 

Acetic  acid.  .  . 
Formic  acid  .  . 
Benzene  

273  +  16.7 
273  +  8.5 
273+  4.9 

43.2ft 
55.6ft 
29.1J 

38.8 
28.4 
53.0 

38.6 
27.7 
50.0 

Nitrobenzene  . 

273+  5.3 

22.3J; 

69.5 

70.7 

Let  us  add,  that  from  the  lowering  found  for  ethylene  bromide, 
117.9,  the  latent  heat  of  fusion  of  this  substance,  unknown  at 
that  time,  was  calculated  to  be  13,  and  that  the  determination 
which  Pettersson  very  kindly  carried  out  at  my  request  gave, 
in  fact,  the  value  expected  (mean,  12.94). 

9.   --   APPLICATION      OF      AVOGADRO'S      LAW      TO      SOLUTIONS. 
GULDBERG    AND   WAAGE's    LAW. 

Having  given  the  physical  side  of  the  problem  the  greater 
prominence,  thus  far,  in  order  to  furnish  the  greatest  possible 
support  to  the  principles  developed,  it  now  remains  to  apply 
it  to  chemistry.  The  most  obvious  application  of  the  law  of 
Avogadro  for  solutions,  as  for  gases,  is  to  ascertain  the  molecu- 
lar weight  of  dissolved  substances.  This  application  has,  in- 
deed, already  been  made,  only  it  consists  not  in  the  investiga- 
tion of  pressures  as  with  gases,  where  every  determination  of 
molecular  weight  amounts  to  the  determination  of  pressure, 
volume,  temperature,  and  weight.  In  solutions  we  would  have 
to  deal  in  such  an  experimental  arrangement,  with  the  deter- 
mination of  the  osmotic  pressure,  and  the  practical  means  of 
determining  this  are  still  wanting.  Yet  this  obstacle  can  be 
overcome  by  determining,  instead  of  the  osmotic  pressure,  one  of 
the  two  values  which,  from  what  is  given  above,  are  connected 
with  it,  i.  e.,  the  diminution  of  vapor-pressure  or  the  lowering 
of  the  freezing-point.  To  this  end  there  is  the  proposition 

*  Ann.  CMm.  Phys.,  (5),  2§,  (6),  11. 
f  Berthelot,  Essai  de  Mecanique  Chimique. 
j  Pettersson,  Journ.  prakt.  Chim,  (2),  24,  129. 
31     ' 


MEMOIRS    ON 


of  Racult  already  made  use  of  for  determining  molecular 
weights  —  viz.,  the  relative  lowering  of  vapor  -  pressure  of  a 
one-per-cent.  aqueous  solution  is  to  be  divided  into  0.185,  or 
the  freezing-point  lowering  is  to  be  divided  into  18.5,  a  method 
which  is  comparable  with  those  used  for  such  determinations 
with  gases,  and  the  results  of  which,  therefore,  confirm  Avoga- 
dro's  law  for  solutions. 

It  is  still  more  remarkable  that  the  so  general  law  of  Guld- 
berg  andWaage,  assumed  also  for  solutions,  can,  in  fact,  be  de- 
veloped as  a  simple  conclusion  from  the  laws  adduced  above  for 
dilute  solutions.  It  is  only  necessary  to  complete  a  reversible 
cycle  at  constant  temperature,  which  can  be  done  with  semi- 
permeable  walls,  as  well  with  solutions  as  with  gases. 

Let  us  imagine  two  systems  of  gaseous  or  dissolved  sub- 
stances in  equilibrium,  and  let  us  represent  this  condition,  in 
general,  by  the  following  symbol  : 

a;Ml'  +  al"Ml"+  etc.^<Jf,;4<'Jf,;'+  etc., 
in  which  a  represents  the  number  of   molecules,  and  M  the 
[chemical}  formula.     This  equilibrium  exists  in  two  vessels,  A 

and  B,  at  the  same  temperature,  but 
at  different  concentrations.  We  will 
designate  the  latter  by  the  partial 
pressure,  or  the  osmotic  pressure 
which  each  of  the  substances  in 
question  exercises.  Let  these  press- 
ures in  vessel  A  be,  P\P" .  -P'^P", 
etc.  :  in  B  they  are  larger  by 
dP'ldP'l'...dP'/,dP',fl,Qte. 

The  reversible  cycle,  to  be  carried 
out,  consists  in  this  :  the  mass  of 
the  first  system,  expressed  by  the 
above  symbol,  is  introduced  into 

A  in  kilograms,  while  the  second  is  removed  in  equivalent 
quantity.  Both  have  here  the  concentrations  which  exist  in  A. 
This  transformation  is  so  carried  out  that  every  one  of  the 
substances  in  question  enters  or  leaves  by  means  of  a  suitable 
piston  and  cylinder,  which  is  separated  from  the  vessel  A  by 
a  wall,  permeable  to  this  substance  alone.  If  we  are  dealing 
with  a  solution,  the  cylinders  themselves  are  made  with  a  semi- 
permeable  wall,  and  are  surrounded  with  the  solvent. 

If   this   is   accomplished,  every  part  of  the   second   system 

32 


(5) 


(1) 


Fig.  5 


THE  MODERN  THEORY  OF  SOLUTION 

undergoes  the  change  in  concentration  necessary  to  become 
equal  to  that  which  exists  in  B.  The  work  done,  per  kilo- 
gram-molecule, is,  as  before,  2  AT7;  in  which  A  is  the 

dP 

fraction  of  the  increase  in  pressure,  therefore  here  —  ;    for 

the  amounts  in  question  the  work  done  is  then  %aT  —  . 

The  second  system  just  obtained,  is  now  conducted  over  into 
the  first  by  means  of  the  vessel  B,  exactly  as  above,  at  the  con- 
centrations prevailing  in  B,  and  these  are  finally  changed  into 
the  original  concentrations  existing  in  A,  by  suitable  change  in 
volume. 

Where  we  are  dealing  with  a  cycle  completed  at  constant 
temperature  the  sum  of  the  amounts  of  work  in  question  is 
zero,  and  this  can  be  indicated  by  the  following  equation,  which, 
indeed,  needs  no  explanation  : 


If  we  observe  that  (1)  and  (5)  are  transformations,  in  the  re- 
verse sense,  of  the  same  parts,  with  the  same  mass,  at  the  same 
temperature,  it  follows  that  : 


and,  for  the  same  reasons  : 

(2)+(4)=0; 

from  which  we  conclude  that  : 

(3)  +  (6)=0. 

But  this  leads  immediately  to  the  law  of  Gruldberg  and  Waage. 
The   amount   of   work  (3)  is,  indeed,  from   the   foregoing, 

2  2a,,  T  —  '-',  and  likewise  (6)  is  equal  to  2  2«/  T  —  '-,  whence  it 

follows  :  L       r^_2a/  TdP\  =0; 

-*  ii  •*•  t  / 


On  integration  we  obtain  : 

2  (ati\og  Pll—al  log  Pt)=  constant, 

but  in  this  P  is  proportional  to  the  concentration  or  active 
mass  C,  and  the  latter  can  therefore  be  introduced  instead  of 
the  former  without  destroying  the  constancy  of  the  whole  ex- 
pression. Therefore  : 

2  (alt  log  Cti  —  a,  log  Ct)  =  constant, 
c  33 


MEMOIRS    ON 

which  is  nothing  but  the  Guldberg-Waage  formula  in  logarith- 
mic form. 


10. — DEVIATIONS  FROM  AVOGADRO'S  LAW  IN  SOLUTIONS.      VARI- 
ATION FROM  THE  GULDBERG-WAAGE  LAW. 

We  have  tried  to  show  in  the  preceding  portion  of  this  paper, 
the  genetic  connection  which  exists  between  the  Guldberg-Waage 
law  and  the  known  or  newly  established  laws  for  solutions  of 
Boyle,  Henry,  Gay-Lussac,  and  Avogadro.  It  is  the  same  which, 
indeed,  long  ago,  allowed  the  law  of  Guldberg  and  Waage  to  be 
demonstrated  for  gases  on  thermodynamic  grounds. 

It  is  now  a  question  of  further  developing  the  laws  of  chem- 
ical equilibrium,  and,  therefore,  at  first,  we  must  examine  more 
closely  the  real  validity  of  the  three  principles  from  which  the 
law  of  Guldberg  and  Waage  is  derived. 

If  we  are  still  considering  "ideal  solutions,"  a  class  of  phe- 
nomena must  be  dealt  with  which,  from  the  now  clearly  demon- 
strated analogy  between  solutions  and  gases,  are  to  be  classed 
with  the  earlier  so-called  deviations  of  gases  from  Avogadro's 
law.  As  the  pressure  of  the  vapor  of  ammonium  chloride,  for 
example,  was  too  great  in  terms  of  this  law,  so,  also,  in  a  large 
number  of  cases  the  osmotic  pressure  is  abnormally  large  ;  and 
as  was  afterwards  shown,  in  the  first  case  there  is  a  breaking 
down  into  hydrochloric  acid  and  ammonia,  so  also  with  solu- 
tions we  would  naturally  conjecture  that,  in  such  cases,  a 
similar  decomposition  had  taken  place.  Yet  it  must  be  con- 
ceded that  anomalies  of  this  kind,  existing  in  solutions,  are 
much  more  numerous,  and  appear  with  substances  which,  it  is 
difficult  to  assume,  break  down  in  the  usual  way.  Examples  in 
aqueous  solutions  are  most  of  the  salts,  the  strong  acids,  and 
the  strong  bases  ;  and,  therefore,  the  existence  of  the  so-called 
normal  molecular  lowering  of  the  freezing-point  and  diminution 
of  the  vapor -pressure  were  not  discovered  until  Raoult  em- 
ployed the  organic  compounds.  These  substances,  almost 
without  exception,  behave  normally.  It  may,  then,  have  ap- 
peared daring  to  give  Avogadro's  law  for  solutions  such  a 
prominent  place,  and  I  should  not  have  done  so  had  not 
Arrhenius  pointed  out  to  me,  by  letter,  the  probability  that 
salts  and  analogous  substances,  when  in  solution,  break  down 
into  ions.  As  a  matter  of  fact,  as  far  as  investigation  has 

34 


THE  MODERN  THEORY  OF  SOLUTION 

been  carried,  the  solutions  which  obey  the  law  of  Avogadro 
are  non-conductors,  which  indicates  that  they  are  not  broken 
down  into  ions  ;  and  a  further  experimental  examination  of  the 
other  solutions  is  possible,  since,  from  the  assumption  made 
by  Arrhenins,  the  deviation  from  Avogadro's  law  can  be  cal- 
culated from  the  conductivity. 

However  this  may  be,  the  attempt  will  now  be  made  to  take 
into  account  these  so-called  deviations  from  Avogadro's  law, 
and,  retaining  the  laws  of  Boyle  and  Gay-Lussac  for  solutions, 
to  give  the  development,  thus  made  possible,  of  Guldberg  and 
Waage's  formula.  The  change  which  the  expressions  hitherto 
developed  undergo,  can  be  made  easily  and  briefly  when  what 
is  stated  above  is  taken  into  account. 

The  combined  expression  of  the  laws  of  Boyle,  Gay-Lussac, 
and  Avogadro  developed  on  page  25  : 

APV=2T, 
is  changed  into  : 

APV=2iT, 

where  the  pressure  is  in  general  i  times  the  value  presupposed 
in  the  above  expression. 

Therefore,  the  work  done  by  reversible  change  in  solutions 
will  be  i  times  the  former  value,  and  this  sums  up  the  entire 
transformation  to  be  introduced,  which  is  then  easily  applied 
to  the  development  of  the  Guldberg  and  Waage  formula  just 
given. 

If  we  return  to  the  relation  obtained  at  the  end  of  the  com- 
pleted cycle,  page  33  : 

(3)  +  (6)=0, 
the  amounts  of  work  done,  (3)  and  (6),  which  were  formerly 

represented  by  220,,  T-  —  ^and—  2  2atT  —  ',  are  now  expressed 
by  i  times  these  respective  values.  The  result  is  consequently  : 


After  integration  we  have  : 

S  (a^i,,  log  Pu—  ai,  log  P,)=  constant, 

and  by  introducing  the  concentration  or  active  mass  C,  instead 
of  the  pressure  which  is  proportional  to  it  : 

2  (allill\QgCn—  ait  log  Ct)=  constant. 

This  is,  then,  the  logarithmic  statement  of  the  Guldberg- 
Waage  formula  in  its  new  form,  which  differs  from  the  earlier 

35 


MEMOIRS    ON 

form  only  in  that  it  contains  the  quantity  i.  It  now  remains  to 
show  that  the  newly  obtained  relation  agrees  very  much  better 
with  the  facts  than  the  original  expression.  It  is,  therefore, 
necessary  to  know  exactly  the  values  of  i,  in  question,  and  in 
this  we  are  limited  to  aqueous  solutions,  since  only  here  is 
there  sufficient  experimental  data  at  hand  to  make  the  exami- 
nation desired. 


11. — DETERMINATION   OF   I   FOR   AQUEOUS   SOLUTIONS. 

Since  we  have  succeeded  in  establishing  Avogadro's  law  for 
solutions  in  four  different  ways,  there  are  also  four  ways  of 
studying  the  deviations  referred  to,  therefore  of  determining  i. 
But  of  these,  that  which  depends  upon  the  lowering  of  the 
freezing-point  so  far  surpasses  the  others,  due  to  the  extended 
and  careful  investigations  in  this  field,  that  we  can  limit  our- 
selves entirely  to  this  method. 

Let  us  then  return  to  the  cycle  which,  on  the  basis  of  freez- 
ing-point determinations,  led  us  to  Avogadro's  law.  This  gave 
the  relation : 

loom 

rp       — *   •*  > 

in  which  the  second  term  represents  the  work  done  by  revers- 
ibly  removing  that  amount  of  the  solvent  which  contains  a 
kilogram-molecule  dissolved  in  it.  This  must  then  be  multi- 
plied by  i : 

100JFZ 
~yr-=^iT. 

From  this  there  appears  at  once  a  very  simple  way  of  deter- 
mining i.  This  value,  from  the  above  equation,  seems  to  be 
proportional  to  t,  i.  e.,  to  the  molecular  lowering  of  the  freez- 
ing-point, since  all  other  values  (T,  absolute  temperature  of 
fusion — W,  latent  heat  of  fusion  of  solvent)  are  constant.  But 
18.5  is  the  molecular  lowering  of  the  freezing-point  for  cane- 
sugar,  which,  from  page  25,  rigidly  obeys  the  law  of  Avogadro, 
and  for  which,  therefore,  i  =  l.  The  value  of  i  for  other  sub- 
stances is,  therefore,  the  lowering  produced  by  them,  divided 
by  18.5.  Almost  exactly  the  same  result  is  obtained  if,  in  the 
above  equation,  for  J'and  W  the  corresponding  values  for  ice, 
273  and  79,  respectively,  are  introduced.  They  will,  therefore, 
be  used  in  the  following  calculations. 

36 


THE  MODERN  THEORY  OF  SOLUTION 


12. — PROOF  OF  THE  MODIFIED   GULDBERG-WAAGE   LAW. 

In  using  the  relation  now  proposed,  and  in  the  comparison 
with  the  results  of  the  Guldberg -Waage  formula  to  be  made 
by  the  reader,  it  is  necessary  to  mention  briefly  the  differ- 
ent forms  which  the  latter  has  taken  in  the  course  of  time. 
We  will  first  represent  our  relation  by  a  simple  formula, 
in  which  also  Guldberg  and  Waage's  conceptions  can  be  ex- 
pressed, viz. : 

2ailogC=K.  (1) 

It  differs  from  the  expression  on  page  35  only  in  this,  the 
terms  referring  to  the  constituent  parts  of  the  two  systems 
are  regarded  with  inverse  signs.  The  original  expression  of 
the  Swedish*  investigators f  is,  then,  very  similar  to  the  above: 

2klogC=£:,  (2) 

only  that  here  k  is  to  be  determined  for  each  constituent  in 
question  by  observing  the  equilibrium  of  the  system. 

But  when  Guldberg  and  Waage  repeatedly  found  the  coef- 
ficient in  question  k,  to  be  equal  to  1,  in  the  observations! 
which  they  had  made  bearing  upon  this  point,  they  gave  their 
law  the  simplified  form: 

SlogC^JT.  (3) 

In  their  last  communication, §  however,  the  change  is  intro- 
duced which  takes  into  account  also  the  number  of  molecules 
#,  and  therefore  the  following  relation  obtains,  corresponding 
to  the  formula  since  developed  for  gases  on  thermodynamic 
grounds : 

2a\ogC=K.  (4) 

We  have,  therefore,  designated  this  above  as  the  Guldberg- 
Waage  formula. 

Although  this  simplified  expression,  with  coefficients  which 
are  whole  numbers,  was  defended  for  solutions  by  the  Swedish 
Investigators,  Lemoine,||  on  the  basis  of  Schloesing's  experi- 
ments on  the  solubility  of  calcium  carbonate  in  water  contain- 
ing carbon  dioxide,  returned,  not  long  ago,  to  the  original 

*  [Guldberg  and  Waage  are  Professors  in  the  University  of  Christiania.] 
f  Christiania  Videnskabs  SelsJcabs  Forhandlingar,  1864. 
\  fitudes  sur  les  affinity  chimiques,  1867. 
§  Journ.  prakt.  Chem.,  19,  69. 
H  Etudes  sur  les  equilibres  c/iimiques,  266. 

37 


MEMOIRS    ON 

formula  (2),  with  coefficients  which  remain  to  be  more  accu- 
rately determined,  but  which  were,  in  general,  not  whole  num- 
bers; and,  indeed,  if  whole  numbers  were  employed,  there  was 
not  an  agreement  between  fact  and  theory. 

In  view  of  this  uncertainty,  the  formula  which  we  have  intro- 
duced has  the  advantage  that  the  coefficients  which  appear  in 
it  are  completely  determined  at  the  outset,  and  therefore  their 
correctness  can  be  decided  at  once  by  experiment.  It  will,  in 
fact,  become  apparent  that  in  the  cases  studied  by  Guldberg 
and  Waage,  through  the  peculiar  values  of  i,  the  simple  form 
brought  forward  by  these  investigators  as  of  general  appli- 
cability, is  completely  verified,  and  the  fact  that  such  simplifi- 
cation is  in  most  cases  permissible  is  in  accordance  with  what 
we  have  laid  stress  upon  above  —  viz.,  the  validity  of  Avo- 
gadro's  law  for  solutions.  On  the  other  hand,  the  investiga- 
tion of  Schloesing,  brought  prominently  forward  by  Lemoine, 
would  show  that  the  simplification  in  question  is  not  allowable, 
since  with  it  the  same  fractional  coefficients  appeared  which 
Schloesing  obtained. 

Before  we  can  proceed  to  examine  our  relation  more  closely, 
it  is  necessary  to  adapt  it  also  to  the  case  where,  in  part,  undis- 
solved  substances  are  present.  This  is  very  simply  done,  and 
leads  to  the  same  result  for  all  of  the  above-mentioned  formulas ; 
if  we  consider  that  such  substances  are  present  in  the  solu- 
tion, even  to  saturation,  therefore  at  constant  concentration. 
All  such  concentrations  can  then  be  transferred  from  the  first 
term  of  the  above  equation  to  the  second,  without  destroying 
the  constancy  of  the  latter.  All  remains,  then,  exactly  the  same, 
only  that  the  dissolved  substances  are  to  be  considered  exclu- 
sively in  the  first  term. 

1.  We  will  first  examine  the  observations  of  Guldberg  and 
Waage.  These  investigators  studied  chiefly  the  equilibrium 
expressed  by  the  following  symbol : 

Ba  CO^+K2  SO,  ^zb  Ba  S0,+  K2  C03, 
and  found,  corresponding  to  their  simplified  formula  : 
log  Cx.soi— log  Cs;2co3  =  K. 

But  from  our  equation  almost  exactly  the  same  relation  re- 
sults, since  for  JT2  $04,  a  =  l  and  i=%.ll ;  for  K2  CO&  a  — I  and 
i'=2.26;  therefore: 

log  CK.SO.— 1.07  log  CK^CO^K. 

The  same  agreement  exists  between  the  two  results,  in  case  we 

38 


THE  MODERN  THEORY  OF  SOLUTION 

are  dealing  with  the  sodium  salts,  since  where  i  for  Na2  80+ 
and  3?<2  C03  is  1.91  and  2.18  respectively,  we  obtain  the  follow- 
ing relation  : 

1  og  CNa*  so,.  —  1  •  1  4  log  C  NO*  co3  =  K. 

2.  But  in  the  above-mentioned  experiments  of  Schloesing* 
we  do  not  expect  these  nearly  integral  numbers.     It  was  a 
question  there  of  the  solubility  of  calcium  carbonate  in  water 
containing  carbon  dioxide,  therefore  of  an  equilibrium  which 
can  be  expressed  by  the  following  symbol  : 

Ca  C03+H2  C03  ^±T  Ca  (HC03)2. 

We  expect,  then,  since  i=I  for  carbon  dioxide,  and  {=2.56  for 
acid  calcium  carbonate: 

0.39  log  Cif,c03  —  log  CCa(HCO^  =  K, 

while  Schloesing  found  the  following  relation  : 

0.37866  log  <7tf2co3-log  CCa(HCo3)2=K. 

The  agreement  is  also  very  satisfactory  for  the  corresponding 

phenomenon  with  barium,  since  i  for  acid  barium  carbonate 

being  2.66,  we  obtain: 

0.376  log  Cn2co3—  log 

while  experiment  gave  •. 

0.38045  log  Cn2co3—  log 

3.  Let  us  now  turn  to  Thomson's  experiments  f  on  the  action 
of  sulphuric  acid  on  sodium  nitrate  in  solution.     This  investi- 
gator arrived  at  the  result  that  the  state  of  the  case  as  foreseen 
by  Guldberg  and  Waage  actually  obtains.     But  this  is,  indeed, 
another  one   of  the  cases  where  our  relation  and  Guldberg- 
Waage's  formula  lead  to  the  same  result. 

If  we  express  the  equilibrium  in  question  by  the  following 
smbol  : 


Guldberg-Waage's  relation  requires: 

log  (?Aa8Sr04  +  log  CHN03~  log  CyaHSO^  —  log 

But: 

iNoy.  504  =  1  .91,  /^iV03  =  l'94,  iAraff5O4  =  l-8 

and  we  obtain  then  : 

1.05  log  Cya>sOi+  1-06  log  CW  jfoj-l.03  log  CNanso. 


which  amounts  to  almost  the  same  thing. 

*  Compt.  rend.,  74,  1552  ;  75,  70. 
f  Thermocliemiscli  Untersuchungen,  1. 
39 


MEMOIRS    ON 

If,  on  the  other  hand,  we  express  the  equilibrium  by  the  fol- 
lowing symbol  : 


Guldberg  and  Waage  would  have  : 

logCVoa^+Blog  CW03  —  log  CH,SOi  — 

while  we  obtain  : 

log  CV^o4  +  2.03  log  CW3-1.07  log  CH.SO. 


thus,  again,  an  almost  perfect  agreement. 

4.  The  investigations  of  Ostwald*  on  the  action  of  hydro- 
chloric acid  on  zinc  sulphide,  which  relate  to  the  equilibrium 
expressed  by  the  following  symbol  : 

Zn  S+2H  Cl  ^±  H2S+Zn  C12, 
leads  us,  by  taking  into  account  the  fact  that  : 


to  the  relation : 

3.96  log  <7#cz— 1.04 log  Cn2s-2.53  log 
Where  at  the  beginning  only  hydrochloric  acid  and  zinc  sul- 
phide were  present,  the  concentrations  of  hydrogen  sulphide 
and  zinc  chloride  in  this  series  of  experiments  are  evidently 
equal.  The  result  would  then  be  so  expressed  that  the  orig- 
inal concentration  of  the  hydrochloric  acid  would  be  given  by 
the  volume  ( F),  in  which  a  known  amount  of  this  substance 
was  present,  while  the  fraction  (x)  denoted  that  portion  which, 
by  contact  with  zinc  sulphide,  had  been  finally  transformed  into 
zinc  chloride.  We  obtain  accordingly : 

3. 96  logi^- 3. 57  log -^constant; 
and  therefore  also : 

—--—F0-n= constant. 


This  function  appears,  in  fact,  to  be  nearly  constant  : 


VOLUME  (7). 
1 

UNTRANSFORMED 
PART  (X). 

0.0411 

2  

0.0380 

4.. 

.  0.0345 

0.0430 
0.0428 
0.0418 
8 0.0317  0.0413 

*  Journ.  prakt.  Chem.,  (2),  19,  480. 
40 


THE    MODERN    THEORY    OF    SOLUTION 

The  analogous  experiments  with  sulphuric  acid,  where  i  for 
H2SOt  and  Zn  80^  is  2.06  and  0.98  respectively,  gave,  simi- 
larly : 

x 


(l-z) 


]7°-°a—  constant, 


which  amounts,  therefore,  to  nearly  a  constant  value  for  x. 
This  is  also,  in  fact,  the  experimental  result,  as  is  shown  by 
the  following  table  : 

.  Tr%  UNTRANSFORMED 

VOLUME  (7).  PART(*). 

2  ..........................  0.0238 

4  ..........................  0.0237 

8  ............  ..............  0.0240 

16  ..........................  0.0241 

5.  The  experiments  of  Engel*  also  merit  consideration.     In 
these,  the  question  is  as  to  the  solubility  of  magnesium  car- 
bonate in  water  containing  carbon  dioxide,  therefore  of  the 
following  equilibrium  : 

Mg  C03+H2  C03  ^±:  Mg  (HC03)2. 

Since  i  for  magnesium  dicarbonate  is  2.64,  our  formula  leads 
here  to  the  following  relation  : 

0.379  log  <7tf2o>3-log 
while  that  observed  was  : 

0.37  log  CWaCOa—  log 

6.  The  experiments  of  the  same  author,  f  on  the  simulta- 
neous solubility  of  ammonium  and  copper  sulphates,  should 
also  be  mentioned  here,  in  -which  we  have  to  deal  essentially 
with  the  equilibrium  : 

Cu  S04+  (NH4)2  SO,  ^±  (NHJ2  Cu  (S04)2. 
Since  the  double  salt  was  always  present  partially  undissolved, 
and  since  i  for  Cu  S04  and  (NH±)2  S0±  is  0.98  and  2,  respective- 
ly, we  obtain  here  the  relation  : 

0.49  log  C  cu  so,  -flog  C 
while  that  found  was  : 

0.438  log  C 


*  Compt.  rend.,  1OO,  352,  444. 
\lbid.,  102,113. 
41 


MEMOIRS    ON 

7.  Finally,  we  mention  the  experiments  of  Le  Ohatelier*  on 
the  equilibrium  between  basic  mercury  sulphate  and  sulphuric 
acid,  which  is  expressed  by  the  following  symbol : 

ffffs  ##6  +  2  H2  S04  ^±  3  Hg  #04  +  2  H2  0. 
In  this  case,  where  i  for  H2  S04  and  Hg  S04  is  2.06  and  0.98,  re- 
spectively, we  expect  the  following  relation  : 

1 . 4  log  CH2  sot — log  Cog  so^ — K, 
while  that  observed  was : 

1.58  log  <7tfaso4  — log  CHgsot  =  K. 
A  very  satisfactory  agreement,  in  general,  is  thus  indicated. 

AMSTERDAM,  September,  1887. 

JACOBUS  HENDRICUS  VAN'T  HOFF  was  born  August  30, 
1852,  at  Rotterdam.  He  received  the  degree  of  Doctor  of 
Philosophy  from  Utrecht  in  1874,  having  studied  at  the  Poly- 
technic Institute  in  Delft  from  1869  to  1871,  at  the  University 
of  Leyden  in  1871,  at  Bonn  with  Kekule  in  1872,  with  Wiirtz 
in  Paris  in  1873,  and  with  Mulder  in  Utrecht  in  1874. 

He  was  made  privat- decent  at  the  veterinary  college  in 
Utrecht  in  1876,  and  in  1878  professor  of  chemistry,  mineral- 
ogy, and  geology  at  the  university  in  Amsterdam.  The  latter 
position  he  held  until  about  two  years  ago,  when  he  was  called 
to  a  chair  created  for  him  in  the  University  of  Berlin. 

Probably  the  best  known  work  of  Van't  Hoff  is  La  Chimie 
dans  VEspace,  which  was  the  origin  of  that  branch  of  chemistry 
which  has  come  to  be.  known  as  stereochemistry.  He  pointed 
out  here  that  whenever  a  compound  is  optically  active,  it  al- 
ways contains  at  least  one  "asymmetric"  carbon  atom,  i.e., 
a  carbon  atom  in  combination  with  four  different  elements  or 
groups.  This  book  appeared  first  in  Dutch  in  1874,  a  year 
later  in  French,  and  has  recently  been  enlarged  and  translated 
into  English.  Other  books  by  Van't  Hoff  which  should  be 
mentioned  are :  Views  on  Organic  Chemistry,  Ten  Years  in  the 
History  of  a  Theory,  Studies  in  Chemical  Dynamics,  revised 
and  enlarged  by  Cohen,  and  translated  into  English  by  Ewan 
— one  of  Van't  HofFs  most  valuable  contributions  to  science  ; 
Lectures  on  the  Formation  and  Decomposition  of  Double  Salts, 
and  Lectures  on  Theoretical  and  Physical  Chemistry,  which  is 
just  appearing. 

*  Compt.  rend.,  97,  1555. 
42 


THE    MODERN    THEORY    OF    SOLUTION 

The  number  of  papers  published  by  Yan't  Hoff  is  not  very 
large,  indeed,  unusually  small,  for  one  who  is  so  well  known. 
That  on  Solid  Solutions  and  the  Determination  of  the  Molec- 
ular Weight  of  Solids,*  opened  up  a  field  in  which  a  number 
have  subsequently  worked. 

*  Ztichr.  Fhys.  Chem.,  5,  322. 


ON   THE   DISSOCIATION  OF  SUBSTANCES 
DISSOLVED  IN  WATER 

BY 

SVANTE  ARRHENIUS 
Professor  of  Physics  in  the  Stockholm  High  School 

Zeitschrift  fur  Phynkalische  CJiemie,  1,  631, 1887 
45 


CONTENTS 

PAGE 

Van't  Hoffs  Law 47 

Exceptions   to  Van't  Hoff's  Law 48 

Two  Methods  of  Calculating  the  Van't  Hoff  Constant  "i" 49 

Comparison  of  Results  by  the  Two  Methods 50 

Additive  Nature  of  Dilute  Solutions  of  Salts 57 

Heats  of  Neutralization 59 

Specific  Volume  and  Specific  Gravity  of  Dilute  Solutions  of  Salts 61 

Specific  Refmctimty  of  Solutions 62 

Conductivity 63 

Lowering  of  Freezing -Point 65 


ON  THE   DISSOCIATION  OF  SUBSTANCES 
DISSOLVED  IN  WATEE* 

BY 

SVAXTE  AREHENIUS 

\y>v* 

IN  a  paper  submitted  to  the  Swedish  Academy  of  Sciences, 
on  the  14th  of  October,  1805,  Van't  Hoff  proved  experimen- 
tally, as  well  as  theoretically,  the  following  unusually  significant 
generalization  of  Avogadro's  law:f 

"The  pressure  which  a  gas  exerts  at  a  given  temperature,  if 
a  definite  number  of  molecules  is  contained  in  a  definite  vol- 
ume, is  equal  to  the  osmotic  pressure  which  is  produced  by 
most  substances  under  the  same  conditions,  if  they  are  dis- 
solved in  any  given  liquid." 

Van't  Hoff  has  proved  this  law  in  a  manner  which  scarcely 
leaves  any  doubt  as  to  its  absolute  correctness.  But  a  diffi- 
culty which  still  remains  to  be  overcome,  is  that  the  law  in 
question  holds  only  for  "most  substances";  a  very  consider- 
able number  of  the  aqueous  solutions  investigated  furnishing 
exceptions,  and  in  the  sense  that  they  exert  a  much  greater 
osmotic  pressure  than  would  be  required  from  the  law  re- 
ferred to. 

If  a  gas  shows  such  a  deviation  from  the  law  of  Avogadro, 
it  is  explained  by  assuming  that  the  gas  is  in  a  state  of  dis- 
sociation. The  conduct  of  chlorine,  bromine,  and  iodine,  at 
higher  temperatures  is  a  very  well-known  example.  We  re- 
gard these  substances  under  such  conditions  as  broken  down 
into  simple  atoms. 

*  Ztschr.  Phys.  CJiem.,  1,  631,  1887. 

f  Van't  Hoff,  Une  propriete  generate  de  la  matidre  diluee,  p.  43  ;  Sv. 
Vet-Ak-s  Handlingar,  21,  Nr.  17,  1886.  [Also  in  Archives  Neerlandaises 
for  1885.] 

47 


MEMOIRS    ON 

The  same  expedient  may,  of  course,  be -marie  use  of  to  explain 
the  exceptions  to  Van't  Hoff's  law  ;  but  it  has  not  been  put  for- 
ward up  to  the  present,  probably  on  account  of  the  newness  of 
the  subject,  the  many  exceptions  known,  and  the  vigorous  objec- 
tions which  would  be  raised  from  the  chemical  side,  to  such  an 
explanation.  The  purpose  of  the  following  lines  is  to  show  that 
such  an  assumption,  of  the  dissociation  of  certain  substances 
dissolved  in  water,  is  strongly  supported  by  the  conclusions 
drawn  from  the  electrical  properties  of  the  same  substances,  and 
that  also  the  objections  to  it  from  the  chemical  side  are  dimin- 
ished on  more  careful  examination. 

In  order  to  explain  the  electrical  phenomena  we  must  assume 
with  Clausius*  that  some  of  the  molecules  of  an  electrolyte  are 
dissociated  into  their  ions,  which  move  independently  of  one 
another.  But  since  the  "osmotic  pressure "  which  a  substance 
dissolved  in  a  liquid  exerts  against  the  walls  of  the  confining 
vessel,  must  be  regarded,  in  accordance  with  the  modern  ki- 
netic view,  as  produced  by  the  impacts  of  the  smallest  parts  of 
this  substance,  as  they  move,  against  the  walls  of  the  vessel, 
we  must,  therefore,  assume,  in  accordance  with  this  view,  that 
a  molecule  dissociated  in  the  manner  given  above,  exercises  as 
great  a  pressure  against  the  walls  of  the  vessel  as  its  ions 
would  do  in  the  free  condition.  If,  then,  we  could  calculate 
what  fraction  of  the  molecules  of  an  electrolyte  is  dissociated 
into  ions,  we  should  be  able  to  calculate  the  osmotic  pressure 
from  Van't  Hoff's  law. 

In  a  former  communication  "  On  the  Electrical  Conductivity 
of  Electrolytes,"  I  have  designated  those  molecules  whose  ions 
are  independent  of  one  another  in  their  movements,  as  active ; 
the  remaining  molecules,  whose  ions  are  firmly  combined  with 
one  another,  as  inactive.  I  have  also  maintained  it  as  probable, 
that  in  extreme  dilution  all  the  inactive  molecules  of  an  elec- 
trolyte are  transformed  into  active.f  This  assumption  I  will 
make  the  basis  of  the  calculations  now  to  be  carried  out.  I 
have  designated  the  relation  between  the  number  of  active 
molecules  and  the  sum  of  the  active  and  inactive  molecules, 
as  the  activity  coefficient. J  The  activity  coefficient  of  an 

*  Clansius,  Pong.  Ann.,  1O1,  347  (1857);  Wied.  Elektr.,  2,  941. 
f  Bihang  der  Stockholmer  Akademie,  8,  Nr.  13  and  14,  2  Tl.  pp.  5  and  13 ; 
1  Tl.,  p.  61. 

tt.«.,2Tl.,p.5. 

48 


THE    MODERN    THEORY    OF    SOLUTION 

electrolyte  at  infinite  dilution  is  therefore  taken  as  unity.  For 
smaller  dilution  it  is  less  than  one,  and  from  the  principles 
established  in  my  work  already  cited,  it  can  be  regarded  as 
equal  to  the  ratio  of  the  actual  molecular  conductivity  of  the 
solution  to  the  maximum  limiting  value  which  the  molecular 
conductivity  of  the  same  solution  approaches  with  increasing 
dilution.  This  obtains  for  solutions  which  are  not  too  concen- 
trated (i.e.,  for  solutions  in  which  disturbing  conditions,  such 
as  internal  friction,  etc.,  can  be  disregarded). 

If  this  activity  coefficient  (a)  is  known,  we  can  calculate  as 
follows  the  values  of  the  coefficient  i  tabulated  by  Yan't  Hoff. 
i  is  the  relation  between  the  osmotic  pressure  actually  exerted 
by  a  substance  and  the  osmotic  pressure  which  it  would  exert 
if  it  consisted  only  of  inactive  (undissociated)  molecules,  i  is 
evidently  equal  to  the  sum  of  the  number  of  inactive  mole- 
cules, plus  the  number  of  ions,  divided  by  the  sum  of  the  inac- 
tive and  active  molecules.  If,  then,  m  represents  the  number 
of  inactive,  and  n  the  number  of  active  molecules,  and  k  the 
number  of  ions  into  which  every  active  molecule  dissociates 
(e.g.,  k=2  for  K  Cl,  i.  e.,  K  and  Cl;  k=3  for  Ba  Clz  and 
K2  SO  i,  i.  e.,  Ba,  Cl,  Cl,  and  K,  K,  £04),  then  we  have  : 

._m+kn 
m  +  n 
But  since  the  activity  coefficient  (a)  can,  evidently,  be  written 

n 
m-\-ri 

Part  of  the  figures  given  below  (those  in  the  last  column), 
were  calculated  from  this  formula. 

On  the  other  hand,  i  can  be  calculated  as  follows  from  the 
results  of  Raoult's  experiments  on  the  freezing-point  of  solu- 
tions, making  use  of  the  principles  stated  by  Yan't  Hoff.  The 
lowering  (t)  of  the  freezing-point  of  water  (in  degrees  Celsius), 
produced  by  dissolving  a  gram-molecule  of  the  given  substance 
in  one  litre  of  water,  is  divided  by  18.5.  The  values  of  i  thus 

calculated,  i  =  —'—,  are  recorded  in  next  to  the  last  column. 
18.5 

All  the  figures  given  below  are  calculated  on  the  assumption 
that  one  gram  of  the  substance  to  be  investigated  was  dissolved 
in  one  litre  of  water  (as  was  done  in  the  experiments  of 
Raoult). 

D  49 


MEMOIRS    ON 

In  the  following  table  the  name  and  chemical  formula  of  the 
substance  investigated  are  given  in  the  first  two  columns,  the 
value  of  the  activity  coefficient  in  the  third  (Lodge's  dissocia- 
tion ratio*),  and  in  the  last  two  the  values  of  i  calculated  by  the 

two  methods:  i= and  i  —  !  +  (&  —  l)a. 

18.5 

The  substances  investigated  are  grouped  together  under  four 
chief  divisions  :  1,  non-conductors  ;  2,  bases  ;  3,  acids  ;  and  4, 

salts. 


NON-CONDUCTORS. 

SUBSTANCE.                              FORMULA.                 a  i=—-.  1 

18.5  i-r(K—i)a. 

Methyl  alcohol CH3  OH           0.00  0.94  1.00 

Ethyl  alcohol C2H5OH       -0.00  0.94  1.00 

Butyl  alcohol C'4H9OH         0.00  0.93  1.00 

Glycerin C3H5(OH)3    0.00  0.92  1.00 

Mannite 06HU06          0.00  0.97  1.00 

Invert  sugar 06H1206          0.00  1.04  1.00 

Cane-sugar 0}2H220U        0.00  1.00  1.00 

Phenol C6H5OH         0.00  0.84  1.00 

Acetone 03H60             0.00  0.92  1.00 

Ethyl  ether (C2H5)20        0.00  0.90  1.00 

Ethyl  acetate O^HQ02            0.00  0.96  1.00 

Acetamide C2H3ONH2     0.00  0.96  1.00 

BASES. 

t  i— 

SUBSTANCE.                             FORMULA.               a  ^=^~^-  i    i(t~  1\ 

18.5  l~r  (A  —  I)  a. 

Barium  hydroxide Ba(OH)2         0.84  2.69  2.67 

Strontium  hydroxide. ..   Sr  (OH)2         0.86  2.61  2.72 

Calcium  hydroxide  ....    Ca(OH)2         0.80  2,59  2.59 

Lithium  hydroxide Li  OH              0.83  2.02  1.83 

•Sodium  hydroxide Na  OH             0.88  1.96  1.88 

Potassium  hydroxide  ..   K OH               0.93  1.91  1.93 

Thallium  hydroxide  ...    Tl  OH              0.90  1.79  1.90 
Tetramethylammonium 

hydrate (CH^NOH  1.99 

*  Lodge,  On  Electrolysis,  Report  of  British  Association,  Aberdeen,  1885, 
p.  756  (London,  1886). 

50 


THE    MODERN   THEORY    OF    SOLUTION 

BASES— (continued). 

t  i= 

8DBSTANCE.                            FORMULA.               fit  *=18~5*  1+ (&  —  !)« 

Tetraethylammonium 

hydrate (^#5)4 &OH  0.92  1.92 

Ammonia "  XH3                   0.01  1.03  1.01 

Metliylamine Cff3  NH2          0.03  1.00  1.03 

Trimethylamiiie (ON3)3N          0.03  1.09  1.03 

Ethylamhie C2H5XH2        0.04  1.00  1.04 

Propylamine C3H,^H2        0.04  1.00  1.04 

Aniline C&H,NH2        0.00  0.83  1.00 

ACIDS. 

t  i= 

SUBSTANCE.                             FORMULA.                a  *  =  j"tt~='  !+(&  —  I)  a 

Hydrochloric  acid H  Cl                  0.90  1.98  1.90 

Hydrobromic  acid H Br                 0.94  2.03  1.94 

Hydroiodicacid HI                    0.96  2.03  1.96 

Hydrofluosilicic  acid...   H2SiF6            0.75  2.46  1.75 

Nitric  acid H N03               0.92  1.94  1.92 

Chloric  acid HCW3             0.91  1.97  1.91 

Perchloric  acid HCIO±              0.94  2.09  1.94 

Sulphuric  acid H280±              0.60  2,06  2.19 

Selenic  acid H2SeO,            0.66  2.10  2.31 

Phosphoric  acid H^PO^              0.08  2.32  1.24 

Sulphurous  acid H2SO^              0.14  1.03  1.28 

Hydrogen  sulphide ....   H2  8                  0.00  1.04  1.00 

lodic  acid HI03               0.73  1.30  1.73 

Phosphorous  acid P  (Off)3          0.46  1.29  1.46 

Boric  acid B(OH)3           0.00  1.11  1.00 

Hydrocyanic  acid H  CN  '            0.00  1.05  1.00 

Formic  acid HCOOH        0.03  1.04  1.03 

Acetic  acid Cff3  CO  OH    0.01  1.03  1.01 

Butyric  acid C3H,COOH  0.01  1.01  1.01 

Oxalic  acid (CO  OH)2        0.25  1.25  1.49 

Tartaricacid C\ffB06            0.06  1.05  1.11 

Malic  acid O4H605            0.04  1.08  1.07 

Lactic  acid C3H603            0.03  1.01  1.03 


MEMOIRS    ON 

SALTS. 

SUBSTANCE.                             FORMULA.  a  i^  l  +  (jfcI1)a. 

Potassium  chloride KCl  0.86  1.82  1.86 

Sodium  chloride NaCl  0.82  1.90  1.82 

Lithium  chloride Li  Cl  0.75  1.99  1.75 

Ammonium  chloride.  . .  NH^  Cl  0.84  1.88  1.84 

Potassium  iodide KI  0.92  1.90  1.92 

Potassium   bromide K Br  0.92  1.90  1.92 

Potassium  cyanide KCN  0.88  1.74  1.88 

Potassium  nitrate K N03  0.81  1.67  1.81 

Sodium  nitrate Na  N03  0.82  1.82  1.82 

Ammonium  nitrate Nff4N03  0.81  1.73  1.81 

Potassium  acetate CH^COOK  0.83  1.86  1.83 

Sodium  acetate CH3COONa  0.79  1.73  1.79 

Potassium  formate HCOOK  0.83  1.90  1.83 

Silver  nitrate Ag N03  0.86  1.60  1.86 

Potassium  chlorate K  Cl  03  0.83  1.78  1.83 

Potassium  carbonate...  K2C03  0.69  2.26  2.38 

Sodium  carbonate Na2C03  0.61  2.18  2.22 

Potassium  sulphate K2  £04  0.67  2.11  2.33 

Sodium  sulphate. Na2S04  0.62  1.91  2.24 

Ammonium  sulphate...  (NffJ2S04  0.59  2.00  2.17 

Potassium  oxalate K2C20±  0.66  2.43  2.32 

Barium  chloride Ba  C12  0.77  2.63  2.54 

Strontium  chloride Sr  C12  0.75  2.76  2.50 

Calcium  chloride Ca  C12  0.75  2.70  2.50 

Cupric  chloride Cu  C12  2.58 

Zinc  chloride ZnCl*  0.70  2.40 

Barium  nitrate Ba(N03)2  0.57  2.19  2.13 

Strontium  nitrate Sr  N03)2  0.62  2.23  2.23 

Calcium  nitrate Ca(N03\  0.67  2,02  2.33 

Lead  nitrate PI  (N03)2  0.54  2.02  2,08 

Magnesium  sulphate..  .  Mg  S0±  0.40  1.04  1.40 

Ferrous  sulphate Fe  80^  0.35  1.00  1.35 

Copper  sulphate Cu  SO*  0.35  0.97  1.35 

Zinc  sulphate Zn  S04  0.38  0.98  1.38 

Cupric  acetate (C2H3  02)2  Cu  0.33  1.68  1.66 

Magnesium  chloride...  Mg  C12  0.70  2.64  2.40 

Mercuric  chloride Hg  C12  0.03  1.11  1.05 

Cadmium  iodide Cd I2  0.28  0.94  1.56 

Cadmium  nitrate..... .  Cd(N03)2  0.73  2.32  2.46 

Cadmium  sulphate....  Cd  SO.  0.35  0.75  1.35 

52 


THE    MODERN    THEORY    OF 

The  last  three  numbers  in  next  to  the  last  column  are  not 
taken,  like  all  the  others,  from  the  work  of  Raoult,*  but  from 
the  older  data  of  Riidorff,t  who  employed  in  his  experiments 
very  large  quantities  of  the  substance  investigated,  therefore 
no  very  great  accuracy  can  be  claimed  for  these  three  numbers. 
The  value  of  a  is  calculated  from  the  results  of  Kohlrausch,J 
Ostwald  §  (for  acids  and  bases),  and  some  few  from  those  of 
Grotrian||  and  Klein. ^[  The  values  of  a,  calculated  from  the 
results  of  Ostwald,  are  by  far  the  most  certain,  since  the  two 
quantities  which  give  a  can,  in  this  case,  be  easily  determined 
with  a  fair  degree  of  accuracy.  The  errors  in  the  values  of  i, 
calculated  from  such  values  of  a,  cannot  be  more  than  5  per 
cent.  The  values  of  a  and  i,  calculated  from  the  data  of  Kohl- 
rausch,  are  somewhat  uncertain,  mainly  because  it  is  difficult 
to  calculate  accurately  the  maximum  value  of  the  molecular 
conducting  power.  This  applies,  to  a  still  greater  extent,  to  the 
values  of  a  and  i  calculated  from  the  experimental  data  of 
Grotrian  and  Klein.  The  latter  may  contain  errors  of  from  10 
to  15  per  cent,  in  unfavorable  cases.  It  is  difficult  to  estimate 
the  degree  of  accuracy  of  Rao ult's  results.  From  the  results 
themselves,  for  very  nearly  related  substances,  errors  of  5  per 
cent.,  or  even  somewhat  more,  do  not  appear  to  be  improbable. 

It  should  be  observed  that,  for  the  sake  of  completeness,  all 
substances  are  given  in  the  above  table  for  which  even  a  fairly 
accurate  calculation  of  i  by  the  two  methods  was  possible.  If 
now  and  then  data  are  wanting  for  the  conductivity  of  a  sub- 
stance (cupric  chloride  and  tetramethylammonium  hydrate), 
such  are  calculated,  for  the  sake  of  comparison,  from  data  for 
a  very  nearly  related  substance  (zinc  chloride  and  tetraethylam- 
monium  hydrate),  whose  electrical  properties  cannot  differ  ap- 
preciably from  those  of  the  substance  in  question. 

Among  the  values  of  i  which  show  a  very  large  difference 
from  one  another,  those  for  hydrofluosilicic  acid  must  be 

*  Raoult,  Ann.  Chim.  Phys.,  [5],  28,  133  (1883) ;  [6],  2,  66,  99,  115 
(1884);  [6].  4,  401  (1885).  [This  volume,  p.  52.] 

t  Riidorff,  Ostwald's  Lehrb.  all.  Chem.,  L,  414. 

j  Kohlrausch,  Wied.  Ann.,  6, 1  and  145  (1879);  26,  161  (1885). 

§  Ostwald,  Journ.  prakt.  Chem.,  [2],  32,  300(1885) ;  [2],  33,  352  (1886) ; 
Ztschr.  PJiys.  Chem.,  1,  74  and  97  (1887). 

fl  Grotrian.  Wied.  Ann.,  18.  177  (1883). 

1  Klein,  Wied.  Ann.,  27,  151  (1886). 

53 


MEMOIRS    ON 

especially  mentioned.  But  Ostwald  has,  indeed,  shown  that 
in  all  probability,  this  acid  is  partly  broken  down  in  aqueous 
solution  into  §HF  and  Si02,  which  would  explain  the  large 
value  of  i  given  by  the  Raoult  method. 

There  is  one  condition  which  interferes,  possibly  very  seri- 
ously, with  directly  comparing  the  figures  in  the  last  two  col- 
umns— namely,  that  the  values  really  hold  for  different  temper- 
atures. All  the  figures  in  next  to  the  last  column  hold,  indeed, 
for  temperatures  only  a  very  little  below  0°C.,  since  they  were 
obtained  from  experiments  on  inconsiderable  lowerings  of  the 
freezing-point  of  water.  On  the  other  hand,  the  figures  of  the 
last  column  for  acids  and  bases  (Ostwald's  experiments)  hold  at 
25°,  the  others  at  18°.  The  figures  of  the  last  column  for  non- 
conductors hold,  of  course,  also  at  0°C.,  since  these  substances 
at  this  temperature  do  not  consist,  to  any  appreciable  extent, 
of  dissociated  (active)  molecules. 

An  especially  marked  parallelism  appears,*  beyond  doubt, 
on  comparing  the  figures  in  the  last  two  columns.  This  shows, 
a  posteriori,  that  in  all  probability  the  assumptions  on  which  I 
have  based  the  calculation  of  these  figures  are,  in  the  main, 
correct.  These  assumptions  were  : 

1.  That  Van't  HoflPs  law  holds  not  only  for  most,  but  for  all 
substances,  even  for  those  which  have  hitherto  been  regarded  as 
exceptions  (electrolytes  in  aqueous  solution). 

2.  That  every  electrolyte  (in  aqueous  solution),  consists  partly 
of  active  (in  electrical  and  chemical  relation),  and  partly  of 
inactive  molecules,  the  latter  passing  into  active  molecules  on 
increasing  the  dilution,  so  that  in  infinitely  dilute  solutions 
only  active  molecules  exist. 

The  objections  which  can  probably  be  raised  from  the  chemi- 
cal side  are  essentially  the  same  which  have  been  brought  for- 
ward against  the  hypothesis  of  Clausius,  and  which  I  have 
earlier  sought  to  show,  were  completely  untenable. f  A  repe- 
tition of  these  objections  would,  then,  be  almost  superfluous.  I 
will  call  attention  to  only  one  point.  Although  the  dissolved 
substance  exercises  an  osmotic  pressure  against  the  wall  of  the 
vessel,  just  as  if  it  were  partly  dissociated  into  its  ions,  yet 

*  In  reference  to  some  salts  which  are  distinctly  exceptions,  compare 
below,  p.  55. 

f  1.  c.,  2  Tl.,  pp.  6  and  31. 

54 


THE    MODERN    THEORY   OF    SOLUTION 

the  dissociation  with  which  we  are  here  dealing  is  not  exactly 
the  same  as  that  which  exists  when,  e.g.,  an  ammonium  salt 
is  decomposed  at  a  higher  temperature.  The  products  of 
dissociation  in  the  first  case  (the  ions)  are  charged  with  very 
large  quantities  of  electricity  of  opposite  kind,  whence  cer- 
tain conditions  appear  (the  incompressibility  of  electricity), 
from  which,  it  follows  that  the  ions  cannot  be  separated  from 
one  another  to  any  great  extent,  without  a  large  expenditure 
of  energy.*  On  the  contrary,  in  ordinary  dissociation  where  no 
such  conditions  exist,  the  products  of  dissociation  can,  in  gen- 
eral, be  separated  from  one  another. 

The  above  two  assumptions  are  of  the  very  widest  significance, 
not  only  in  their  theoretical  relation,  of  which  more  hereafter, 
but  also,  to  the  highest  degree,  in  a  practical  sense.  If  it  could, 
for  instance,  be  shown  that  the  law  of  Van't  Hoff  is  generally 
applicable — which  I  have  tried  to  show  is  highly  probable — the 
chemist  would  have  at  his  disposal  an  extraordinarily  conven- 
ient means  of  determining  the  molecular  weight  of  every  sub- 
stance soluble  in  a  liquid. f 

At  the  same  time,  I  wish  to  call  attention  to  the  fact 
that  the  above  equation  (1)  shows  a  connection  between  the 
two  values  i  and  a,  which  play  the  chief  roles  in  the  two 
chemical  theories  developed  very  recently  by  Van't  Hoff  and 
myself. 

I  have  tacitly  assumed  in  the  calculation  of  ?,  carried  out 
above,  that  the  inactive  molecules  exist  in  the  solution  as  sim- 
ple molecules  and  not  united  into  larger  molecular  complexes. 
The  result  of  this  calculation  (i.  e.,  the  figures  in  the  last  col- 
umn), compared  with  the  results  of  direct  observation  (the  fig- 
ures in  next  to  the  last  column),  shows  that,  in  general,  this 
supposition  is  perfectly  justified.  If  this  were  not  true  the 
figures  in  next  to  the  last  column  would,  of  course,  prove  to 
be  smaller  than  in  the  last.  An  exception,  where  the  latter 
undoubtedly  takes  place,  is  found  in  the  group  of  sulphates 
of  the  magnesium  series  (Mg  SO^  Fe  S0±,  Cu  #04,  Zn  80^  and 
Cd  504),  also  in  cadmium  iodide.  We  can  assume,  to  explain 
this,  that  the  inactive  molecules  of  these  salts  are,  in  part, 

*l.c,  2Tl.,p.  8. 

f  This  means  has  already  been  employed.  Compare  Ruoult,  Ann. 
Chim.  Phys.t  [6],  8,  317  (1886) ;  Pateru6  and  Nasini,  Ber.  deutsctt.  chem. 
Gesell,  1886,  2527. 

55 


MEMOIRS    ON 

combined  with  one  another.  Hittorf,*  as  is  well  known,  was  led 
to  this  assumption  for  cadmium  iodide,  through  the  large  change 
in  the  migration  number.  And  if  we  examine  his  tables  more 
closely  we  will  find,  also,  an  unusually  large  change  of  this  num- 
ber for  the  three  of  the  above-named  sulphates  (Mg  $04,  Cu  S04, 
and  Zn  jSO±)  which  he  investigated.  It  is  then  very  probable 
that  this  explanation  holds  for  the  salts  referred  to.  But  we 
must  assume  that  double  molecules  exist  only  to  a  very  slight 
extent  in  the  other, salts.  It  still  remains,  however,  to  indicate 
briefly  the  reasons  which  have  led  earlier  authors  to  the  assump- 
tion of  the  general  existence  of  complex  molecules  in  solution. 
Since,  in  general,  substances  in  the  gaseous  state  consist  of  sim- 
ple molecules  (from  Avogadro's  law),  and  since  a  slight  increase  in 
the  density  of  gases  often  occurs  near  the  point  of  condensation, 
indicating  a  union  of  the  molecules,  we  are  inclined  to  see  in 
the  change  of  the  state  of  aggregation,  such  combinations  tak- 
ing place  to  a  much  greater  extent.  That  is,  we  assume  that 
the  liquid  molecules  in  general  are  not  simple.  I  will  not  com- 
bat the  correctness  of  this  conclusion  here.  But  a  great  differ- 
ence arises  if  this  liquid  is  dissolved  in  another  (e.g.,  H Cl  in 
water).  For  if  we  assume  that  by  dilution  the  molecules  which 
were  inactive  at  the  beginning  become  active,  the  ions  being  sep- 
arated to  a  certain  extent  from  one  another,  which  of  course  re- 
quires a  large  expenditure  of  energy,  it  is  not  difficult  to  assume, 
also,  that  the  molecular  complexes  break  down,  for  the  most  part, 
on  mixing  with  water,  which  in  any  case  does  not  require  very 
much  work.  The  consumption  of  heat  on  diluting  solutions 
has  been  interpreted  as  a  proof  of  the  existence  of  molecular 
complexes.f  But,  as  stated,  this  can  also  be  ascribed  to  the 
conversion  of  inactive  into  active  molecules.  Further,  some 
chemists,  to  support  the  idea  of  constant  valence,  would  as- 
sume 1  molecular  complexes,  in  which  the  unsaturated  bonds 
could  become  saturated.  But  the  doctrine  of  constant  valence 
is  so  much  disputed  that  we  are  scarcely  justified  in  basing  any 
conclusions  upon  it.  The  conclusions  thus  arrived  at,  that,  e.g., 
potassium  chloride  would  have  the  formula  (KCl)3,  L.  Meyer 

*  Hittorf,  Pogg.  Ann.,  1O6,  547  and  551  (1859) ;   Wied.  Elektr.,  2,  584. 
f  Ostwald,  Lebrb.  all.  Chem.,  I.,  811;   L.  Meyer,  Moderne  Theorien  der 
Chemie,  p.  319  (1880). 
\  L.  Meyer,  1.  c.  p.  360. 

56 


THE    MODERN    THEORY    OF    SOLUTION 

sought  to  support  by  the  fact  that  potassium  chloride  is  much 
less  volatile  than  mercuric  chloride,  although  the  former  has  a 
much  smaller  molecular  weight  than  the  latter.  Independent 
of  the  theoretical  weakness  of  such  an  argument,  this  conclu- 
sion could,  of  course,  hold  only  for  the  pure  substances,  not  for 
solutions.  Several  other  reasons  have  been  brought  forward  by 
L.  Meyer  for  the  existence  of  molecular  complexes,  e.g.,  the 
fact  that  sodium  chloride  diffuses  more  slowly  than  hydrochloric 
acid,*  but  this  is  probably  to  be  referred  to  the  greater  friction 
(according  to  electrical  determinations),  of  sodium  against  water, 
than  of  hydrogen.  But  it  suffices  to  cite  L.  Meyer's  own  words  : 
"Although  all  of  these  different  points  of  departure  for  ascer- 
taining molecular  weights  in  the  liquid  condition  are  still  so 
incomplete  and  uncertain,  nevertheless  they  permit  us  to  hope 
that  it  will  be  possible  in  the  future  to  ascertain  the  size  of 
molecules,  "f  But  the  law  of  Van't  Hoff  gives  entirely  reliable 
points  of  departure,  and  these  show  that  in  almost  all  cases  the 
number  of  molecular  complexes  in  solutions  can  be  disregarded, 
while  they  confirm  the  existence  of  such  in  some  few  cases,  and, 
indeed,  in  those  in  which  there  were  formerly  reasons  for  as- 
suming the  existence  of  such  complexes.];  Let  us,  then,  not 
deny  the  possibility  that  such  molecular  complexes  also  exist 
in  solutions  of  other  salts — and  especially  in  concentrated  solu- 
tions ;  but  in  solutions  of  such  dilution  as  was  investigated 
by  Raoult,  they  are,  in  general,  present  in  such  small  quantity 
that  they  can  be  disregarded  without  appreciable  error  in  the 
above  calculations. 

Most  of  the  properties  of  dilute  solutions  of  salts  are  of  a 
so-called  additive  nature.  In  other  words,  these  properties 
(expressed  in  figures)  can  be  regarded  as  a  sum  of  the  proper- 
ties of  the  parts  of  the  solution  (of  the  solvent,  and  of  the  parts 
of  the  molecules,  which  are,  indeed,  the  ions).  As  an  example, 
the  conductivity  of  a  solution  of  a  salt  can  be  regarded  as  the 
sum  of  the  conductivities  of  the  solvent  (which  in  most  cases 
is  zero),  of  the  positive  ion,  and  of  the  negative  ion.§  In 
most  cases  this  is  controlled  by  comparing  two  salts  of  one 

*  L.  Meyer,  1.  c.  p.  316. 

f  L.  Meyer,  L  c.  p.  321.  The  law  of  Van't  Hoff  makes  this  possible,  as 
is  shown  above. 

\  Hittorf,  I.  c.  Ostwald's  Lelirb.  all.  Cliern.,  p.  816. 
§  Kohlrausch,  Wied.  Ann.,  167  (1879). 

57 


MEMOIRS    ON 

acid  (e.g.,  potassium  and  sodium  chlorides)  with  two  corre- 
sponding salts  of  the  same  metals  with  another  acid  (e.  g.,  potas- 
sium and  sodium  nitrates).  Then  the  property  of  the  first  salt 
(K  CT),  minus  the  property  of  the  second  (Na  Cl),  is  equal  to 
the  property  of  the  third  (KN03),  minus  the  property  of  the 
fourth  (NaN03).  This  holds  in  most  cases  for  several  proper- 
ties, such  as  conductivity,  lowering  of  freezing-point,  refrac- 
tion equivalent,  heat  of  neutralization,  etc.,  which  we  will  treat 
briefly,  later  on.  It  finds  its  explanation  in  the  nearly  com- 
plete dissociation  of  most  salts  into  their  ions,  which  was  shown 
above  to  be  true.  If  a  salt  (in  aqueous  solution)  is  completely 
broken  down  into  its  ions,  most  of  the  properties  of  this  salt 
can,  of  course,  be  expressed  as  the  sum  of  the  properties  of 
the  ions,  since  the  ions  are  independent  of  one  another  in  most 
cases,  and  since  every  ion  has,  therefore,  a  characteristic  prop- 
erty, independent  of  the  nature  of  the  opposite  ion  with  which 
it  occurs.  The  solutions  which  we,  in  fact,  investigate  are 
never  completely  dissociated,  so  that  the  above  statement 
does  not  hold  rigidly.  But  if  we  consider  such  salts  as  are 
80  to  90  per  cent,  dissociated  (salts  of  the  strong  bases  with  the 
strong  acids,  almost  without  exception),  we  will,  in  general,  not 
make  very  large  errors  if  we  calculate  the  properties  on  the 
assumption  that  the  salts  are  completely  broken  down  into 
their  ions.  From  the  above  table  this  evidently  holds  also 
for  the  strong  bases  and  acids :  Ba  (OH)2,  Sr  (OH)2,  Ca  (OH)2, 
Li  OH,  Na  OH,  K  OH,  Tl  OH,  and  H  Cl,  H Br,  HI,  H NO.,, 
HC103,  and  #C704. 

But  there  is  another  group  of  substances  which,  for  the  most 
part,  have  played  a  subordinate  role  in  the  investigations  up  to 
the  present,  and  which  are  far  from  completely  dissociated,  even 
in  dilute  solutions.  Examples  taken  from  the  above  table  are, 
the  salts,  Hg  C12  (and  other  salts  of  mercury),  Cd  T2,  Cd  S04, 
Fe  S04,  Mg  S0±,  Zn  S0±,  Cu  S0±,  and  Cu  (C2  H3  02)2;  the  weak 
bases  and  acids,  as  NH3,  and  the  different  amines,  H3  P04,  H2  8, 
B  (OH)3,  H  CN,  formic,  acetic,  butyric,  tartaric,  malic,  and  lac- 
tic acids.  The  properties  of  these  substances  will  not,  in  gen- 
eral, be  of  the  same  (additive)  nature  as  those  of  the  former 
class,  a  fact  which  is  completely  confirmed,  as  we  will  show 
later.  There  are,  of  course,  a  number  of  substances  lying 
between  these  two  groups,  as  is  also  shown  by  the  above 
table.  Let  attention  be  here  called  to  the  fact  that  several 

58 


THE    MODERN    THEORY    OF    SOLUTION 

investigators  have  been  led  to  the  assumption  of  a  certain  kind 
of  complete  dissociation  of  salts  into  their  ions,  by  considering 
that  the  properties  of  substances  of  the  first  group,  which  have 
been  investigated  far  more  frequently  than  those  of  the  second, 
are  almost  always  of  an  additive  nature.*  But  since  no  reason 
could  be  discovered  from  the  chemical  side  why  salt  molecules 
should  break  down  (into  their  ions)  in  a  perfectly  definite 
manner,  and,  moreover,  since  chemists,  for  certain  reasons  not 
to  be  more  fully  considered  here,  have  fought  as  long  as  pos- 
sible against  the  existence  of  so-called  unsaturated  radicals 
(under  which  head  the  ions  must  be  placed),  and  since,  in 
addition,  it  cannot  be  denied  that  the  grounds  for  such  an  as- 
sumption were  somewhat  uncertain,!  the  assumption  of  com- 
plete dissociation  has  not  met  with  any  hearty  approval  up  to 
the  present.  The  above  table  shows,  also,  that  the  aversion  of 
the  chemist  to  the  idea  advanced,  of  complete  dissociation,  has 
not  been  without  a  certain  justification,  since  at  the  dilutions 
actually  employed,  the  dissociation  is  never  complete,  and  even 
for  a  large  number  of  electrolytes,  (the  second  group)  is  rela- 
tively inconsiderable. 

After  these  observations  we  now  pass  to  the  special  cases  in 
which  additive  properties  occur. 

1.  The  Heat  of  Neutralization  in  Dilute  Solutions. — When 
an  acid  is  neutralized  with  a  base,  the  energies  of  these  two 
substances  are  set  free  in  the  form  of  heat;  on  the  other  hand, 
a  certain  amount  of  heat  disappears  as  such,  equivalent  to  the 
energies  of  the  water  and  salt  (ions)  formed.  We  designate 
with  (  )  the  energies  for  those  substances,  for  which  it  is  unim- 
portant for  the  deduction  whether  they  exist  as  ions  or  not, 
and  with  [  ]  the  energies  of  the  ions,  which  always  means  the 
energies  in  dilute  solution.  To  take  an  example,  the  follow- 
ing amounts  of  heat  are  set  free  on  neutralizing  Na  OH  with 
|  H,  S04  (1),  and  with  H  Cl  (2),  and  on  neutralizing  K  OH  with 
\  H.2S04  (3),  and  with  H  Cl  (4)  (all  in  equivalent  quantities, 
and  on  the  previous  assumption  of  a  complete  dissociation  of 
the  salts) : 

*Valson,  Compt.  rend.,  73,  441  (1871);  74,  103  (1872);  Favre  and 
Valson,  Compt.  rend.,  75,  1033  (1872);  Raoult,  Ann.  Chim.  Phys.,  [6], 
4,  426. 

f  In  reference  to  the  different  hypotheses  of  Raoult,  compare,  I.  c., 
p.  401. 

59 


MEMOIRS    ON 


(Na  OH)  +  (H  01)  -  (H,  0)  -  [  Aa]  -  [  Cl]  . 


.  (I) 

(2) 
(3) 

(K  OH)  +  (H  Cl)  -(H,0)-  [AH  -  [  Cl].  (4) 

(1)  —  (2)  is,  of  course,  equal  to  (3)—  (4),  on  the  assumption  of 
a  complete  dissociation  of  the  salts.  This  holds,  approximately, 
as  above  indicated,  in  the  cases  which  actually  occur.  This  is 
all  the  more  true,  since  the  salts  which  are  farthest  removed 
from  complete  dissociation  —  in  this  case  JV#8  $04  and  JTS  $04 
—  are  dissociated  to  approximately  the  same  extent,  therefore 
the  errors  in  the  two  members  of  the  last  equation  are  approxi- 
mately of  equal  value,  a  condition  which,  in  consequence  of 
the  additive  properties,  exists  more  frequently  than  we  could 
otherwise  expect.  The  small  table  given  below  shows  that  the 
additive  properties  distinctly  appear  on  neutralizing  strong  bases 
with  strong  acids.  This  is  no  longer  the  case  with  the  salts  of 
weak  bases  with  weak  acids,  because  they  are,  in  all  probability, 
partly  decomposed  by  the  water. 

HEATS    OF    FORMATION   OF   SOME   SALTS   IN    DILUTE   SOLUTION,  ACCORDING 
TO    THOMSEN    AND   BERTHELOT. 


HCl 
H  Br 
HI 

HN03 

C2  /A  02 

CH202 

i-  (CO  OH)2 

Na  OH.  . 
KOH  
NH,  
iCa(OH),. 
±Ba(OH), 
k8r(OH)t. 

13.7 
13.7 
124 
14.0 
13.8 
14.1 

13.7     (0.0) 
13.8  (  +  0.1) 
12.5(+0.1) 
13.9  (-0.1) 
18.9  (+0.1) 
13.9  (-0.2) 

13.3  (-0.4) 
13.3  (-0.4) 
12.0  (-0.4) 
13.4  (-0.6) 
13.4(-04) 
13.  3  (-0.8) 

13.4  (-0.3) 
13.4(-0.3) 
11.9(-0.5) 
13.5  (-0.5) 
13.5  (-0.3) 
13.5  (-0.6) 

14.3  (+0.6) 
14.3  (+0.6) 
12.7  (+0.3) 

t  #2  SOi 

inss 

HCN 

*  C02 

Na  OH 

15  8  (+2  1) 

3  8  (    99) 

2  9  (     108) 

i  o  2  {      3  ^\ 

KOH 

15  7  (  +  2  0) 

3  8  (—9  9) 

3  0  (  —  10  7) 

10  1  (     36) 

NH3 

14  5  (+2  0) 

3  1  (  —  9  3) 

1  3(  —  11  1) 

5  3  (     71) 

|  Ca(OH)*.  . 
$  Ba(OI-f)9.  . 
i  Sr(Off) 

3.9  (-10.1) 

As  can  be  seen  from  the  figures  inclosed  in  brackets  (which 
represent  the  difference  between  the  heat  tone  in  question  and 
the  corresponding  heat  tone  of  the  chloride),  they  are  approxi- 

60 


THE    MODERN    THEORY    OF    SOLUTION 

mately  constant  in  every  vertical  column.  This  fact  is  very 
closely  connected  with  the  so-called  thermo-neutrality  of  salts  ; 
but  since  I  have  previously  treated  this  subject  more  directly, 
and  have  emphasized  its  close  connection  with  the  Williamson- 
Clausius*  hypothesis,  I  do  not  now  need  to  give  a  detailed 
analysis  of  it. 

2.  Specific  Volume  and  Specific  Gravity  of  Dilute  Salt  Solu- 
tions.— If  a  small  amount  of  salt,  whose  ions  can  be  regarded  as 
completely  independent  of  one  another  in  the  solution,  is  added 
to  a  litre  of  water,  the  volume  of  this  is  changed.  Let  x  be  the 
quantity  of  the  one  ion  added,  and  y  that  of  the  other,  the  vol- 
ume will  be  approximately  equal  to  (\+ax  +  by)  litres,  a  and  b 
being  constants.  But  since  the  ions  are  dissociated  from  one 
another,  the  constant  a  of  the  one  ion  will,  of  course,  be  inde- 
pendent of  the  nature  of  the  other  ion.  The  weight  is,  similar- 
ly, (\  +  cx+dy)  kilograms,  in  which  c  and  d  are  two  other  con- 
stants characteristic  for  the  ions.  The  specific  gravity  will 
then,  for  small  amounts  of  x  and  y,  be  represented  by  the 
formula  : 

l  +  (c-a)x+(b-d)y, 

where,  of  course,  (c  —  a)  and  (b  —  d)  are  also  characteristic  con- 
stants for  the  two  ions.  The  specific  gravity  is,  then,  an  addi- 
tive property  for  dilute  solutions,  as  Valsonf  has  also  found. 
But  since  "specific  gravity  is  not  applicable  to  the  representation 
of  stoichiometric  laws,"  as  Ostwald  ];  maintains,  we  will  refrain 
from  a  more  detailed  discussion  of  these  results.  The  deter- 
mination of  the  constants  a  and  b,  etc.,  promises  much  of  value, 
•  but  thus  far  has  not  been  carried  out. 

The  changes  in  volume  in  neutralization  are  closely  related  to 
these  phenomena.  It  can  be  shown  that  the  change  in  volume 
in  neutralization  is  an  additive  property,  from  considerations 
very  similar  to  those  above  for  heat  of  neutralization.  All 
the  salts  investigated  (K^  Na-  NH^)  are  almost  completely 
dissociated  in  dilute  solutions,  as  is  clear  from  the  above  table 
(and  is  even  clearer  from  the  subsequent  work  of  Ostvvald), 
so  that  a  very  satisfactory  agreement  for  these  salts  can  be 
expected.  The  differences  of  the  change  in  volume  in  the 

*l.  c.,2Tl.,  p.  67. 

f  Valson,  Compt.  rend.,  73,  441  (1871) ;  Ostwald,  Lehrb.  all  Chem.,  I.,  384. 

\  Ostwald,  ibid.,  I.,  386. 

61 


MEMOIRS    ON 

formation  of  the  salts  in  question,  from  nineteen  different  acids, 
are  also  found  to  be  nearly  constant  numbers.*  Since  bases 
which  form  salts  of  the  second  group  have  not  been  investi- 
gated, there  are  no  exceptions  known. 

3.  Specific  Refr activity  of  Solutions. — If  we  represent  by  n 

the  index  of  refraction,  by  d  the  density,  and  by  P  the  weight 

n ^ 

of  a  substance,  P  — —  is,  as  is  well  known,  a  value  which,  when 

added  for  the  different  parts  of  mixtures  of  several  substances, 
gives  the  corresponding  value  for  the  mixture.  Consequently, 
this  value  must  make  the  refraction  equivalent  an  additive 
property  also  for  the  dissociated  salts.  The  investigations  of 
Gladstone  have  shown  distinctly  that  this  is  true.  The  potas- 
sium and  sodium  salts  have  been  investigated  in  this  case  just 
as  the  acids  themselves.  We  take  the  following  short  table 
on  molecular  refraction  equivalents  from  the  Lelirbuch  of  Ost- 
wald :  f 

POTASSIUM.        SODIUM.         HYDROGEN.  K~Na.          K—H. 

Chloride 18.44  15.11  14.44  3.3  4.0 

Bromide 25.34  21.70  20.63  3.6  4.7 

Iodide 35.33  31.59  31.17  3.7  4.2 

Nitrate 21.80  18.66  17.24  3.1  4.5 

Sulphate 30.55  22.45  2x4.1 

Hydrate 12.82  9.21            5.95  3.6  6.8 

Formate 19.93  16.03  13.40  3.9  6.5 

Acetate 27.65  24.05  21.20*  3.6  6.5 

Tartrate 57.60  50.39  45.18         2x3.6  2x6.2 

The  difference  K—Na  is,  as  is  seen,  almost  constant  through- 
out, which  was  also  to  be  expected  from  the  knowledge  of  the 
extent  of  dissociation  of  the  potassium  and  sodium  salts.  The 
same  holds  also  for  the  difference  K—H,  as  long  as  we  are 
dealing  with  the  strong  (dissociated)  acids.  On  the  contrary, 
the  substances  of  the  second  group  (the  slightly  dissociated 
acids),  behave  very  differently,  the  difference  K—H  being  much 
greater  than  for  the  first  group. 

4.  ValsonJ  believed  that  he  also  found  additive  properties 

*  Ostwald,  Lefirb.  all.  Chem.,  I.,  388. 
f  Ostwald,  I.  c.,p.  443. 

i  Valson,  Compt.  rend,,  74,  103(1872) ;  Ostwald,  1.  c.  p.  492. 
62 


THE  MODERN  THEORY  OF  SOLUTION 

of  salt  solutions  in  C&pillary  Phenomena.  But  since  this  can  be 
traced  back  to  the  fact  that  the  specific  gravity  is  an  additive 
property,  as  above  stated,  we  need  not  stop  to  consider  it. 

5.  Conductivity.  —  F.  Kohlrausch,  as  is  well  known,  has  done 
a  very  great  service  for  the  development  of  the  science  of  elec- 
trolysis, by  showing  that  conductivity  is  an  additive  property.* 
Since  we  have  already  pointed  out  how  this  is  to  be  understood, 
we  pass  at  once  to  the  data  obtained.  Kohlransch  gives  in  his 
work  already  cited,  the  following  values  for  dilute  solutions  : 

Li=21,  J#=40,  #=278,  C2=49, 
=  46,  Cl  03=4D, 


But  these  values  hold  only  for  the  most  strongly  dissociated 
substances  (salts  of  the  monobasic  acids  and  the  strong  acids 
and  bases).  For  the  somewhat  less  strongly  dissociated  sul- 
phates and  carbonates  of  the  univalent  metals  (compare  above 
table),  he  obtained,  indeed,  much  smaller  values:  JT  =  40, 
NHt  =  31,  Na  =  22,  Li  =  11,  Ag=32,  #=166,  i#04  =  40, 
£(703=36;  and  for  the  least  dissociated  sulphates  (the  metals 
of  the  magnesium  series),  he  obtained  the  following  still  smaller 
values  :  i  Mg  =  14=f  $Zn=12,  £  Cu  =  12,  %SO±=22. 

It  appears,  then,  that  the  law  of  Kohlrausch  holds  only 
for  the  most  strongly  dissociated  salts,  the  less  strongly  disso- 
ciated giving  very  different  values.  But  since  the  number  of 
active  molecules  also  increases  with  increase  in  dilution,  so 
that  at  extreme  dilution  all  salts  break  down  completely  into 
active  (dissociated)  molecules,  it  would  be  expected  that,  at 
higher  dilutions,  the  salts  would  behave  more  regularly.  I 
showed,  also,  from  some  examples  that  "  we  must  not  lay  too 
much  stress  upon  the  anomalous  behavior  of  salts  (acetates  and 
sulphates)  of  the  magnesium  series,  since  these  anomalies  dis- 
appear at  greater  dilutions.  "f  I  also  believed  I  could  establish 
the  view  that  conductivity  is  an  additive  property,  J  and  I  as- 
cribed to  the  conductivity  of  hydrogen  in  all  acids  (even  in  the 
poorest  conducting,  whose  behavior  was  not  at  all  compatible 
with  this  view),  a  value  which  was  entirely  independent  of  the 


*  Kohlrausch,  Wied.  Ann.,  6, 167  (1879);  Wied.  Elek.,  1,  610 ;  2,  955. 
1 1.  c.,  1  Tl.,  p.  41. 
\l.c.,  2Tl.,p.  12. 


MEMOIRS    ON 

nature  of  the  acid.  This,  again,  was  accomplished  only  with  the 
aid  of  the  conception  of  activity.  The  correctness  of  this  view 
appears  still  more  clearly  from  the  later  work  of  Kohlrausch,* 
and  of  Ostwald.  f  Ostwald  attempts  to  show  in  his  last  work 
upon  this  subject,  that  the  view  that  conductivity  is  additive 
is  tenable  without  the  aid  of  the  activity  conception,  and  he 
succeeds  very  well  for  the  salts  which  he  employed  (potassium, 
sodium,  and  lithium),  because  these  are,  in  general,  very  nearly 
completely  dissociated,  and  especially  at  very  great  dilutions. 
This  result  receives  further  support  from  the  fact  that  anal- 
ogous salts  of  the  univalent  metals,  if  they  are  very  closely  re- 
lated to  one  another,  are  dissociated  to  approximately  the  same 
extent  at  the  same  concentrations.  But  if  we  were  dealing 
with  salts  of  less  closely  related  metals  we  should  obtain  very 
different  results,  as  is  shown  distinctly  by  previous  investi- 
gations. As  Ostwald  I  himself  says,  the  law  of  Kohlrausch 
does  not  hold  for  the  acids,  but  we  must  add  to  it  the  con- 
ception of  activity  if  we  would  have  it  hold  true.  But  this 
law  does  not  apply  to  all  salts.  A  closer  investigation  of  cop- 
per acetate  would,  indeed,  lead  to  considerable  difficulties. § 
This  would  be  still  more  pronounced  if  we  took  into  account 
the  mercury  salts,  since  it  appears  from  the  investigations  of 
Grotrian,||  as  if  these  gave  only  a  very  small  fraction  of  the 
conductivity  derived  from  this  law,  even  in  extreme  dilutions. 
It  is  apparent  that  not  all  of  the  salts  of  the  univalent  metals 
conform  to  this  law,  since,  according  to  Bouty,^[  potassium 
antimonyl  tartrate,  in  0.001  normal  solution,  conducts  only 
about  one-fifth  as  well  as  potassium  chloride.  From  the  law 
of  Kohlrausch  it  must  conduct  at  least  half  as  well  as  potas- 
sium chloride.  But  if  we  make  use  of  the  activity  conception, 
the  law  of  Kohlrausch  holds  very  satisfactorily,  as  is  shown 
by  the  values  of  i  in  the  above  table  for  weak  bases  and  acids, 
calculated  on  the  basis  of  this  law,  and  also  for  Hg  C12  and 
Cu(C2Hz  O.^)^-  They  agree  very  well  with  the  values  of  i  de- 
rived from  the  experiments  of  E-aoult. 

*  Kohlrausch,  Wied.  Ann.,  26,  215  and  216  (1885). 
f  Ostwald,  Ztschr.  Phys.  Chem.,  1,  74  and  97  (1887). 
j  Ostwald,  1.  c.  p.  79. 
§  My  work,  already  cited.     1  Tl.,  p.  39. 
||  Grotrian,  Wied.  Ann.,  18,  177  (1883). 
-If  Bouty,  Ann.  Chim.  Phys.,  [6],  3,  472  (1884;. 
64 


THE    MODERN    THEORY    OF    SOLUTION 

G.  Lowering  of  the  Freezing-Point. — Raoult*  shows,  in  one  of 
his  investigations,  that  the  lowering  of  the  freezing-point  of 
water  by  salts  can  be  regarded  as  an  additive  property,  as 
would  be  expected,  in  accordance  with  our  views  for  the  most 
strongly  dissociated  salts  in  dilute  solutions.  The  following 
values  were  obtained  for  the  activities  of  the  ions : 

GROUP. 

1  st.     Univalent  (electro)  negative  ions  (radicals) . .  20  (Cl.  Br,  OH,  N03,  etc.) 

2d.      Bivalent  11(S04.  Cr  04,  etc.) 

3d.      Univalent  (electro)  positive     "         "  15(H,  K,  Na,NIJt,  etc.) 
4th. f  Bivalent  or  polyvalent  "  8(Ba,  Mg,  Al^  etc.) 

But  there  are  very  many  exceptions  which  appear  because  of 
unusually  small  dissociation  even  in  the  most  dilute  solutions, 
as  is  seen  from  the  following  table  : 


Calculated.  Observed. 

Weak  acids. 35  19 

Cu(C2H302)2 48  31.1 

Potassium  antimonyl  tar- 

trate 41  18.4 

Mercuric  chloride..         .  48  20.4 


Calculated.  Observed. 

Lead  acetate 48  22.2 

Aluminium  acetate 128  84.0 

Ferric  acetate 128  58.1 

Platinic  chloride. . .  88  29.0 


We  know,  from  experiments  on  the  electrical  conductivity  of 
those  substances  which  are  given  in  the  first  column,  that  their 


*  Raoult,  Ann.  Chim.  Phys.,  [6],  4,  416  (1885). 

f  All  ions  have  the  same  value  18.5,  according  to  the  views  already  ex- 
plained. Raoult  has,  evidently,  ingeniously  forced  these  substances  under 
the  general  law  of  the  additivity  of  freezing-point  lowering,  by  assigning 
to  the  ions  of  the  less  dissociated  substances,  as  Mg  80t,  much  smaller  values 
(8  and  11  respectively).  The  possibility  of  ascribing  smaller  values  to  the 
polyvalent  ions  is  based  upon  the  fact  that,  in  general,  the  dissociation  of 
salts  is  smaller  the  greater  the  valence  of  their  ions,  as  I  have  previously 
maintained  (1.  c.,  I  Tl.,  p.  69  ;  2  Tl.,  p.  5).  "The  inactivity  (complexity) 
of  a  salt  solution  is  greater,  the  more  easily  the  constituents  of  the 
salt  (acid  and  base)  form  double  compounds."  This  result  is,  moreover, 
completely  confirmed  through  subsequent  work  by  Ostwald  (Ztschr.  Phys. 
Chem.,\,  105  to  109).  It  is  evident  that  if  we  were  to  give  the  correct  value. 
18.5,  to  the  polyvalent  ions,  the  salts  obtained  from  them  would  form 
very  distinct  exceptions.  (Probably  a  similar  view  in  reference  to  other  addi- 
tive properties  could  be  correctly  brought  forward.)  Although  Raoult  has, 
then,  artificially  forced  these  less  strongly  dissociated  salts  to  conform  to 
his  law,  he  has  not  succeeded  in  doing  so  with  all  of  the  salts,  as  is  pointed 
out  above. 

E  65 


MEMOIRS    ON 

molecules  are  very  slightly  dissociated.  The  remaining  sub- 
stances are  closely  related  to  these,  so  that  we  can  expect  them 
to  behave  similarly,  although  they  have  not  been  investigated, 
electrically,  up  to  the  present.  But  if  we  accept  the  point  of 
view  which  I  have  brought  forward,  all  of  these  substances, 
the  latter  as  well  as  the  cases  previously  cited,  are  not  to  be 
regarded  as  exceptions  ;  on.  the  contrary,  they  obey  exactly  the 
same  laws  as  the  other  substances  hitherto  regarded  as  normal. 
Several  other  properties  of  salt  solutions  are  closely  connect- 
ed with  the  lowering  of  the  freezing-point,  as  Goldberg*  and 
Van't  Hofff  have  shown.  These  properties  are  proportional 
to  the  lowering  of  the  freezing-point.  All  of  these  properties 
- — lowering  of  the  vapor -pressure,  osmotic  pressure,  isotonic 
coefficients, —  are,  therefore,  to  be  regarded  as  additive.  De 
VriesJ  has  also  shown  this  for  isotonic  coefficients.  But  since 
all  of  these  properties  can  be  traced  back  to  the  lowering  of  the 
freezing-point,  I  do  not  think  it  necessary  to  enter  into  the 
details  of  them  here. 

SVAKTE  ARRHE^IUS  was  born  February  19,  1859,  near 
tlpsala,  Sweden.  After  leaving  the  Gymnasium  in  1876,  he 
studied  in  the  University  of  Upsala  until  1881.  From  1881  to 
1883  he  worked  at  the  Physical  Institute  of  the  Academy  of 
Sciences  in  Stockholm.  Having  received  the  Degree  of  Doctor 
of  Philosophy  from  the  University  of  Upsala  in  1878,  he  was 
appointed  privat-docent  in  that  institution  in  1884. 

A  little  later,  the  Stockholm  Academy  of  Sciences  granted 
Arrhenius  an  allowance  that  he  might  visit  foreign  universities. 
In  1888  he  worked  with  Van't  Hoff  in  Amsterdam,  in  1889  with 
Ostwald  in  Leipsic,  and  in  J890  with  Boltzmann  in  Gratz. 

In  1891  he  was  called  to  Stockholm  as  a  teacher  of  physics, 
in  what  is  termed  the  Stockholm  High  School,  but  which,  in 
reality,  corresponds  favorably  with  many  of  the  smaller  univer- 
sities abroad.  In  1895  he  was  appointed  to  the  full  professor- 
ship of  physics  in  Stockholm,  a  position  which  he  now  holds. 

Some  of  his  more  important  pieces  of  work,  in  addition  to 

*  Guldberg,  Compt.  Tend.,  7O,  1349  (1870). 
f  Van't  Hoff,  I.  c.  p.  20. 

j  De  Vries,  Erne  Metlwde  zur  Analyse  der  Turgorkraft,  PrinffsheinVs  Jahr- 
biichcr,  14,  519  (1883) ;  Van't  Hoff,  /.  c.  p.  26. 

66  • 


THE    MODERN    THEORY    OF    SOLUTION 

that  included  in  this  volume,  are  :  The  Conductivity  of  Very 
Dilute  Aqueous  Solutions  (Dissertation);  Theory  of  Isohydric 
Solutions  ;  Effect  of  the  Solar  Radiation  on  the  Electrical  Phe- 
nomena in  the  Earth's  Atmosphere;  Effect  of  the  Amount  of 
Carbon  Dioxide  in  the  Air  on  the  Temperature  of  the  Earth's 
Surface. 

Arrhenius  is  also  a  member  of  a  number  of  learned  societies 
and  academies. 


THE  GENERAL  LAW  OF  THE  FREEZING 
OF  SOLVENTS 

BY 

F.  M.  RAOULT 

Professor  of  Chemistry  in  Grenoble. 
(Annales  de  Chimie  et  de  Physique,  [6],  2,  66, 1884.) 


CONTENTS 

PAGE 

Effect  of  Dissolved  Substances  on  Freezing-Points 71 

Solutions  in  Acetic  Acid 73 

Solutions  in  Formic  Acid 77 

Solutions  in  Benzene 78 

Solutions  in  Nitrobenzene 80 

Solutions  in  Ethylene  Bromide 82 

Solutions  in  Water 83 

Conclusions. .  .  88 


THE  GENERAL  LAW  OF  THE  FREEZING 
OF  SOLVENTS  * 

BY 

F.  M.  RAOULT 

IF  we  represent  by  A  the  coefficient  of  lowering  of  a  substance, 
•i.e.,  the  lowering  of  the  freezing-point  produced  by  one  gram 
of  the  substance  dissolved  in  one  hundred  grams  of  the  sol- 
vent ;  by  J/  the  molecular  weight  of  the  compound  dissolved, 
calculated  by  making  in  the  atomic  formula  of  this  compound 
— supposing  it  to  be  an  anhydride — H=l,  0=16,  etc.;  by  T 
the  molecular  lowering  of  freezing — i.e.,  the  lowering  of  the 
freezing-point  produced  by  one  moleculef  of  the  substance 
dissolved  in  100  molecules  of  the  solvent,  we  have : 

MA  =  T. 

I  have  found  that  if  the  solutions  are  dilute,  and  do  not  con- 
tain more  than  one  equivalent];  of  substance  to  a  kilogram  of 
water,  all  the  organic  substances  in  aqueous  solution  produce 
a  molecular  lowering  which  is  nearly  constant,  always  lying 
between  17  and  20,  and  which  usually  approaches  the  mean 
T=IS.5;  and  I  have  shown  (Ann.  C/iim.  Phys.,  January,  1883) 
what  use  could  be  made  of  this  fact  for  determining  the  molec- 
ular weights  of  organic  compounds  soluble  in  water.  I  will 
now  show  that  analogous  results  are  obtained  with  all  solvents 
which  can  be  readily  solidified,  and  that  a  very  important  gen- 
eral law  is  connected  with  them. 

In  the  researches  which  I  shall  discuss  here,  I  have  gener- 
ally employed  very  dilute  solutions,  containing  less  than  one 
molecule  of  substance  in  two  kilograms  of  water. 

*  Ann.  Chim.  Phys.,  [6],  2,  66. 

f  [By  "  one  molecule >:  is  meant  a  number  of  grams  of  the  substance  equal 
to  the  number  expressing  its  ''molecular  iceight."] 

\  [By  "  equivalent  "  i*  meant  the  same  as  "  molecule." — See  above.] 

71 


MEMOIRS    ON 

The  use  of  very  dilute  solutions  oilers  several  advantages. 
First,  it  makes  it  possible  to  avoid,  for  the  most  part,  the  er- 
rors resulting  from  the  more  or  less  arbitrary  opinions  as  to 
the  state  of  the  substance  in  the  solutions,  and  which  result  in 
assigning  to  the  solvent  some  molecules  which,  in  most  cases, 
belong  really  to  the  dissolved  substance.  An  example  will 
make  this  clear. 

If  I  dissolve  6  grams  of  anhydrous  magnesium  sulphate 
(Mg  SO^=120)}  i.e.,  -fa  of  a  molecular  weight,  in  100  grams  of 
water,  I  produce  a  lowering  of  the  freezing-point  of  0°.958. 
But  if  we  admit  that  6.3  grams  of  the  water  are  united  with 
the  dissolved  salt  to  form  a  hydrate  with  7 H20  (which  appears 
to  me  not  very  probable),  the  weight  of  the  water  acting  as  sol- 
vent is  reduced  to  93.7  grams.  We  have,  then,  for  the  molecular 
lowering  of  the  salt : 

T_  0.958  x  120  x93.7  =  1?  95 

GxlOO 

If,  on  the  contrary,  we  suppose  that  the  dissolved  salt  exists  in 
the  anhydrous  state,  we  find : 

y_0.958xl20_19  16 

6 

The  digression  is  relatively  only  -fa ;  and  if  the  first  value  was 
correct,  this  digression  would  still  diminish  with  the  more  di- 
lute solutions,  until  it  almost  completely  disappeared.  An- 
other advantage,  equally  important,  which  results  from  using 
very  dilute  solutions,  is  that  a  sufficient  quantity  of  ice  can  be 
produced  during  the  experiment,  without  greatly  changing  the 
concentration  of  the  solution.  The  result  is,  the  thermometer 
remains  stationary  for  a  long  time,  usually  for  several  minutes, 
and  the  temperature  indicated  can  be  determined  with  the- 
greatest  precision. 

Without  compelling  myself  to  make  all  of  the  solutions  of  the 
same  dilution  (which  would  have  unnecessarily  increased  the 
difficulties),  I  have,  as  far  as  possible,  made  their  dilution  such, 
that  the  lowering  of  the  freezing-point  should  be  between  1° 
and  2°.  This  lowering  is,  indeed,  quite  sufficient,  since  it  can 
be  determined  to  about  -g-J-g-  of  a  degree,  as  I  have  already  ex- 
plained. (Ibid.) 

The  solvents  which  I  have  employed  in  these  researches 

are  : 

72 


THE    MODERN    THEORY    OF    SOLUTION 

FREEZING- 
POINT. 

Water  ...............................  0°.00 

Benzene  .............................  4°,96 

Nitrobenzene  .........................  5°.28 

Ethylene  bromide.  ....................  7°.92 

Formic  acid  ..........................  8°.  52 

Acetic  acid  ...............  :  .  .  .  .  .......  16°.75 

Since  in  the  experiments  on  the  freezing-point  the  cooling  is 
sloiv,  and  since  the  liquid  is  constantly  agitated,  that  portion 
which  solidifies  appears  in  the  form  of  glistening  plates,  or  of 
very  small  crystalline  grains  which  float  in  the  liquid.  It  is  al- 
ways the  pure  solvent  which  separates,  at  least  at  the  beginning 
of  the  freezing  and  under  the  conditions  which  I  employed. 
The  freezing-point  can  thus  be  obtained  by  the  process  indicated, 
with  a  very  great  degree  of  accuracy,  as  well  when  the  solvent 
is  pure  as  wheli  it  contains  a  substance  dissolved  in  it. 

The  lowering  of  the  freezing-point  due  to  the  presence  of  a 
foreign  substance  in  one  of  these  solvents,  is  always  obtained 
by  taking  the  difference  between  the  freezing-point  of  the  solu- 
tion and  that  of  the  pure  solvent,  determined  in  the  same  way, 
and  with  only  a  short  interval  between  the  determinations.  If 
P  is  the  weight  of  the  solvent,  P'  that  of  the  dissolved  substance, 
and  K  the  lowering  of  the  freezing-point  as  obtained  experi- 
mentally, we  have  for  the  coefficient  of  lowering  A,  (i.  e.,  the 
lowering  produced  by  1  gram  of  the  substance  in  100  grams  of 
the  solvent)  : 


P'  X  100 

for  all  of  the  solutions  of  the  dilution  which  I  employed,  thus 
following  the  law  of  Blagden,  at  least  approximately.  The  sub- 
stances to  be  dissolved  are  used  in  as  pure  condition  as  possible, 
and  weighed  with  the  usual  precautions.  If  they  are  volatile 
they  are  weighed  in  bulbs,  which  are  afterwards  broken  by 
shaking  in  the  closed  flasks  containing  a  known  weight  of  the 
solvent. 

SOLUTIONS   IN   ACETIC   ACID. 

Although  acetic  acid  undergoes  very  marked  undercooling,  it 
always  freezes  exactly  at  the  same  temperature  when  in  contact 

73 


MEMOIRS    ON 

with  a  portion  of  the  acid  previously  solidified.  The  crystals 
formed,  although  heavier  than  the  liquid,  float  in  it  during  the 
stirring,  in  the  form  of  glistening  plates.  A  bath  of  water  con- 
taining ice  suffices  to  cool  the  acid,  and  it  must  be  used  in  all 
of  the  experiments. 

Acetic  acid  can  dissolve  a  large  number  of  substances,  partic- 
ularly those  of  an  organic  nature.  It  is  absolutely  necessary 
to  use  this  acid  completely  dehydrated,  i.  e.,  without  any  water, 
for  those  experiments  which  have  to  do  with  hygroscopic  sub- 
stances. But  for  other  substances  an  acid  such  as  is  found 
in  commerce,  containing  from  one  to  two  per  cent,  of  w^ater, 
can  be  used  without  any  inconvenience.  The  compounds  to 
be  dissolved  in  the  acid  ought  always  to  be  dry  and  freed  from 
water  of  crystallization.  Otherwise  the  water  which  they  would 
introduce  into  the  solvent  would  complicate  the  results.  We 
can  avoid  the  difficulty  cf  obtaining  acetic  acid  absolutely 
free  from  water  by  making  several  determinations,  after  having 
added  to  the  same  liquid,  in  succession,  new  quantities  of  the 
substance  to  be  investigated.  If  the  substance  is  very  hygro- 
scopic, the  quantity  first  added  generally  takes  up  the  water 
dissolved  in  the  acid,  and  gives  a  very  small  lowering.  The 
quantities  next  added  find  no  more  water  present,  and  give  a 
constant  lowering.  It  is  the  latter  which  is  adopted.  The  fol- 
lowing table  contains  a  summary  of  my  results : 

TABLE  L* 

Freezing -Point  Lowerings  of  Solutions  in  Acetic  Acid. 

SUBSTANCES   DISSOLVED  MOLECULAR 

IN   ACETIC   ACID.  FORMULAS.  LOWERINGS. 

Methyl  iodide CH3 1  38.8 

Chloroform Off C13  38.6 

Carbon  tetrachloride C  Cl±  38.9 

Carbon  bisulphide OS2  38.4 

Hexane C6ffu  40.1 

Ethylene  chloride C2ff4C12  40.0 

Oil  of  turpentine Olo  ff]6  39.2 

*  The  molecular  weights,  M,  and  the  lowering  coefficients,  A,  are  omitted 
in  this  and  the  following  tables  ;  their  product,  T,  which  is  the  value  of  im- 
portance, being  given. 

74 


THE    MODERN    THEORY    OF    SOLUTION 
TABLE  I.  —  (Continued.) 


Nitrobenzene  ..................    C6H5X02  41.0 

Naphthalene  ..................    O10ff8  39.2 

Methyl  nitrate  .................    Cff3  N03  38.  7 

Methyl  salicylate  ..............    C8H803  39.1 

Ether  ........................    C\HWO  39.4 

Ethyl  sulphide  ................    C\H10M  38.5 

Ethyl  cyanide  .................    C3ff5N  37.6 

Ethyl  formate  .................    O3H602  37.2 

Ethyl  valerate  .................    C  \  H^  02  39.6 

Allyl  snlphocyanate  ............    <74  H5  .¥>S'  38.2 

Aldehyde  .....................    C2H,  0  38.4 

Chloral  .......................    C'2HOC13  39.2 

Benzaldehyde  .................    6'7  H%  0   *  39.7 

Camphor  ......................    OWR160  39.0 

Acetone  ......................    C3  H6  0  38.1 

Acetic  anhydride  ...............    C^H603  36.6 

Formic  acid  ...................    CH2  02  36.5 

Butyric  acid  ...................    C±H802  37.3 

Valeric  acid  ...................    C5H}062  39.2 

Benzoic  acid  ..................    C,H602  43.0 

Camphoric  acid  .......  .-  ........    C\0  H16  04  40.0 

Salicylic  acid  ..................    C,H603  40.5 

Picric  acid  ....................    O6II3N30,  39.8 

Water  .........................   H2  0  33.0 

Methyl  alcohol  .................    CH^  0  35.7 

Ethyl  alcohol  .................    C2  R6  0  36.4 

Butyl  alcohol  ..................    C\HIQ0  38.7 

Amyl  alcohol  ..................    05H120  39.4 

Allyl  alcohol  ...................    C3H6  0  39.1 

Glycerin  .......................    C3ff803  36.2 

Salicin  ........................    C13H180,  37.9 

Santonin  ......................    C\5H1803  38.1 

Phenol  ........................    C6ff6  0  36.2 

Pyrogallol  .....................    O6H603  37.3 

Hydrocyanic  acid  ...............   If  ON  36.6 

Acetamide  .....................    C2H5NO  36.1 

75 


MEMOIRS    ON 


TABLE  I.— (Concluded.} 


SUBSTANCES  DISSOLVED 
IN   ACETIC   ACID. 


MOLECULAR 
FORMULAS.  LOWERINGS. 

T=MA. 

Ammonium  acetate C2  H^  N02  35.0 

Aniline  acetate CQHU  N02  36.2 

Quinine  acetate (724  N32  N2  06  41.0 

Strychnine  acetate C23  H2Q  N2  04  41.6 

Brucine  acetate C25  H^  N2  06  40.0 

Codeine  acetate (720  H2r,  N05  38.3 

Morphine  acetate C38  H^&  N2  0}0  43.0 

Potassium  acetate C2  H3  K02  39.0 

Sulphur  monochloride S2012  38.7 

Arsenic  trichloride As  CI3  41.5 

Tin  tetrachloride Sn  C14  41.3 

Hydrogen  sulphide H2  S  35.6 

Sulphur  dioxide S02  38.5 

ABNORMAL 
LOWERINGS. 

Sulphuric  acid H2  SO^  18.6 

Hydrochloric  acid . . .  „ II  Cl  17.2 

Magnesium  acetate C±H60±  Mg  18.2 

An  examination  of  the  preceding  table  gives  rise  to  two  im- 
portant remarks  : 

1.  For  substances  dissolved  in  acetic  acid  there  is  a  maxi- 
mum molecular  lowering,  wliicli  is  39.     A  few  substances  like 
benzoic   acid  and  morphine  acetate,  have,  it  is  true,  a  low- 
ering as  great  as  43  ;  but  everything  points  to  the  conclusion 
that  this  extraordinary  amount  of  lowering  is  only  apparent, 
and  that  it  results  from  some  chemical  action,  such,  for  exam- 
ple, as  the  combination  of  the  dissolved  substance  with  some 
molecules  of  the  solvent. 

2.  Of  the  fifty-nine  substances  in  this  table,  fifty-six  have 
a  molecular  lowering  between  37  and  41,  and  always  close  to 
39,  which  I  take  as  the  normal  lowering.     Only  three  give  an 
abnormal  lowering,  which  is  close  to  18,  and  is  nearly  half  the 
preceding  value.     These  three  substances,  which  appear  at  the 
end  of  the  list,  are  of  mineral  nature,  and  it  is  to  be  observed 
that  they  are  very  hygroscopic.     Thus  :  The  molecular  lowering s 

76 


THE  MODERN  THEORY  OF  SOLUTION 

produced  by  the  different  compounds  in  acetic  acid  approach  two 
numbers,  39  and  18,  of  which  the  one,  produced  in  the  great  ma- 
jority of  cases,  is  obviously  double  the  other. 

SOLUTIONS  IN   FORMIC   ACID. 

The  formic  acid  which  I  employed  froze  at  8°. 52,  present- 
ing the  same  phenomena  as  acetic  acid.  The  solvent  power  of 
this  acid  appears  to  be  just  as  great  as  that  of  acetic  acid.  It 
seems  to  be  even  greater  for  the  compounds  soluble  in  water. 
But  its  high  price  and  the  difficulty  of  obtaining  it  again  from 
the  solutions  have  prevented  me  from  making  very  extensive 
experiments  with  it.  Table  II.  gives  a  resume  of  the  results 
obtained. 

TABLE  II. 
Freezing- Point  Lowerings  of  Solutions  in  Formic  Acid. 

— 

Chloroform CHC13  26.5  ' 

Benzene CGH6  29.4 

Ether C^H100  28.2 

Aldehyde O2ff,0  26.1 

Acetone C^H6  0  27.8 

Acetic  acid C2  H±  02  26.5 

Brucine  formate Cu  H28  N2  0G  29.7 

Potassium  formate CH K02  28.9 

Arsenic  trichloride As  C13  26.6 

ABNORMAL 
LOWERING.* 

Magnesium  formate C2H04Mg  13.9 

The  above  table  gives  rise  to  two  remarks  already  made  for 
acetic  acid  : 

1.  There  is  a  maximum  of  molecular  lowering  of  the  freezing- 
point  for  substances  dissolved  in  formic  acid,  which  is  about  29. 

2.  The  molecular  loiverings  of  the  freezing-point  produced 
by  the  different  compounds  in  formic  acid  approach  the  two 
numbers  28  and  14,  the  one  being  twice  the  other. 

*  [Unimportant  note  omitted.] 
77 


MEMOIRS    ON 


SOLUTIONS   IN    BENZENE. 

The  benzene  sold  under  the  name  of  crystallizable  benzene,  and 
which  freezes  at  about  5°,  is  nearly  chemically  pure,  and  very 
well  adapted  for  use.  The  results  which  it  gives  do  not  differ 
from  those  obtained  with  the  purest  benzene  made  from  benzoic 
acid.  The  undercooling  which  is  always  produced,  as  in  the 
preceding  liquids,  is  removed  by  contact  with  a  particle  of  solid 
benzene,  and  small  opaque  crystals  of  benzene  are  seen  to  in- 
crease in  number  immediately,  which,  although  more  dense  than 
the  liquid,  float  in  it  during  the  stirring. 

The  results  obtained  are  summarized  in  the  following  table  : 

TABLE  III. 

Freezing -Point  Lowerings  of  Solutions  in  Benzene. 

SUBSTANCES   DISSOLVED  LOWKMNG? 

IN   BENZENE.  FORMULAS.  p-WA 

Methyl  iodide ...../.. Cff3 1  50.4 

Chloroform , CH  C13  51.1 

Carbon  tetrachloride 0  C74  51.2 

Carbon  bisulphide C  82  49.7 

Ethyl  iodide 02H5I  51.0 

Ethyl  bromide C2H5Br  50.2 

Hexane O6HU  51.3 

Ethylene  chloride C2H4C12  48.6 

Oil  of  turpentine O]Q  H16  49.8 

Nitrobenzene C6  H5  N02  48.0 

Naphthalene C\Q HQ  %Q.O 

Anthracene Cu  H]n  51.2 

Methyl  nitrate C  H3  N03  49.3 

Methyl  oxalate O,H60^  49.2 

Methyl  salicylate CBHB03  51.5 

Ether " C\H100  49.7 

Ethyl  sulphide O^H^S  51.8 

Ethyl  cyanide C3ff5N  51.6 

Ethyl  formate O3H602  49.3 

Ethyl  valerate C^H^02  50.0 

Oil  of  mustard C\H5N8  51.4 

Nitroglycerin O3N3H509  49.9 

78 


THE    MODERN    THEORY    OF    SOLUTION 


TABLE  III. — (Continued.) 


SUBSTANCES  DISSOLVED 
IN   BENZENE. 


FORMULAS. 


Tributyrin C}5H2606 

Triolein C51  #]04  06 

Aldehyde C,  H4  0 

Chloral C2HOC13 

Benzaldehyde C\  H6  0 

Camphor Cw  H}6  0 

Acetone C3H60 

Valerone C9  H^  0 

Acetic  anhydride C4H603 

Santonin.    C\5  ff^8  03 

Picric  acid C6H3N30, 

Aniline CBH^N 

Narcotine C22  H23  JVr07 

Codeine ClBH2l  ^03 

Thebaine C19  H2l  N03 

Sulphur  monochloride S2  C12 

Arsenic  trichloride. . .    As  C13 

Phosphorus  trichloride P  C13 

Phosphorus  pentachloride P  C15 

Stannic  chloride Sn  Cl± 

Methyl  alcohol CH,  0 

Ethyl  alcohol, C2H6  0 

Butyl  alcohol O^ffloO 

Amyl  alcohol C5  H12  0 

Phenol C6H60 

Formic  acid CH2  02 

Acetic  acid C2H±02 

Valeric  acid C5  Hw  02 

Benzoic  acid C-  HQ  02 


MOLECULAR 
LOWERINGS. 

T=MA. 

48.7 
49.8 
48.7 
50.3 
50.1 
51.4 
49.3 
51.0 
47.0 
50.2 
49.9 
46.3 
52.1 
48.7 
48.0 
51.1 
49.6 
47.2 
51.6 
48.8 

ABNORMAL 
LOWERINGS. 

25.3 

28.2 

43.2 

39.7 

32.4 

23.2 

25.3     • 

27.1 

25.4 


This  table  gives  rise  to  the  same  remarks  as  the  preced- 
ing. 

1.  For  substances  dissolved  in  benzene  there  is  a  maximum 
lowering  of  the  freezing-point.  This  maximum  lowering  appears 

79 


MEMOIRS    ON 

to  be  about  50.  Some  lowerings,  it  is  true,  are  a  little  above 
this  figure,  but  the  difference  seems  to  me  to  be  due  either  to 
impurities  or  to  some  action  exerted  upon  the  solvent. 

2.  For  the  hydrocarbons  and  their  derivatives,  the  ethers, 
aldehydes,  acetones,  acid  anhydrides,  glucosides,  alcaloids, 
and  chlorides  of  the  metalloids,  the  molecular  lowering  of  the 
freezing-point  in  benzene  lies  between  48  and  51,  and  always 
approaches  49,  a  number  which  ought  to  be  considered  the 
mean  normal  molecular  lowering  in  benzene.  As  to  the  alco- 
hols, phenol,  and  the  acids  (that  is,  the  compounds  which  con- 
tain hydroxyl),  their  molecular  lowering  in  benzene  generally 
lies  between  23  and  27,  and  approaches  the  mean  25,  a  number 
which  is  obviously  half  the  mean  of  the  normal  lowering. 
The  only  hydroxyl  compound  which  produces  the  normal  low- 
ering in  benzene  is  picric  acid ;  but  we  know  that  this  acid 
forms  a  definite  compound  with  the  benzene,  thus  making  it 
an  exceptional  substance.  Two  or  three  alcohols  give  an  in- 
termediate lowering.  We  thus  see  that  in  benzene,  as  in  the 
preceding  solvents,  the  molecular  loiverings  of  the  freezing-point 
of  the  different  compounds  are  grouped  around  two  values,  49 
and  25,  the  one  being,  obviously,  twice  the  other. 

It  should  be  observed  that  the  smaller  of  these  two  values, 
which  appears,  only  exceptionally  with  acetic  and  formic  acids, 
occurs  more  frequently  when  benzene  is  used  as  solvent. 

SOLUTIONS    IN    KITKOBENZENE. 

It  is  difficult  to  find  commercial  nitrobenzene  sufficiently 
pure  for  these  experiments.  I  prepared  the  specimen  which 
I  used.  For  this  purpose  I  treated  pure  benzene  with  nitric 
acid,  at  only  a  slightly  elevated  temperature,  so  as  to  entirely 
avoid  the  production  of  dinitrobenzene.  The  product,  washed 
with  sodium  carbonate  and  water,  was  separated  by  fractional 
distillation  from  the  excess  of  benzene  and  other  impurities. 
The  nitrobenzene  thus  obtained  distils  completely  at  205°, 
and  freezes  at  5°. 28.  Nitrobenzene,  like  the  preceding  sol- 
vents, undergoes  undercooling,  and  in  contact  with  a  solidified 
particle  of  the  same  substance  it  freezes  in  the  form  of  small 
crystals,  which,  notwithstanding  their  great  density,  float  in 
the  liquid  during  the  stirring. 

The  law  relating  to  the  molecular  lowerings  produced  by  the 

80 


THE    MODERN    THEORY    OF    SOLUTION 

different  substances  in  a  given  solvent  being  clearly  estab- 
lished by  the  preceding  experiments,  I  limited  myself  to  ascer- 
tain whether  it  is  verified  with  nitrobenzene.  I  obtained  the 
following  results : 

TABLE  IV. 
Freezing- Point  Lowerings  of  Solutions  in  Nitrobenzene. 

MOLECULAR 

SUBSTANCES  DISSOLVED  FORMULAS.  LOWERING*. 

IN   NITROBENZENE.  T— MA 

Chloroform C H C13  69.9 

Carbon  bisulphide CS2  70.2 

Oil  of  turpentine C\QHIB  69.8 

Benzene C6H6  70.6 

Naphthalene C\0ff8  73.6 

Ether C\HW0  67.4 

Ethyl  valerate C~,HU02  73.2 

Ethyl  acetate C±HQ02  72.2 

Beuzaldehyde O,  H6  0  70.3 

Acetone. C3H60  69.2 

Codeine C\B H2}^03  73.5 

Arsenic  trichloride As  C13  67.5 

Stannic  chloride Sn  Cl±  71.4 

ABNORMAL 
LOWERINGS. 

Methyl  alcohol CHJ)  35.4 

Ethyl  alcohol C,  H6  0  35.6 

Acetic  acid C2H±02  36.1 

Valeric  acid CSHW02  42.4 

Benzoic  acid C-H602  37.7 

\Ve  see  that  the  effects  produced  in  nitrobenzene  by  com- 
pounds of  the  different  chemical  types,  are  exactly  analogous 
to  those  which  the  same  substances  produce  in  benzene. 
There  is  a  maximum  of  the  molecular  lowering,  which  appears  to 
be  close  to  73,  for  the  substances  which  do  not  act  chemically  upon 
the  solvent. 

The    hydrocarbons    and    their    substitution    products,  the 
ethers,  aldehydes,  and    acetones,   and    the    chlorides    of   the 
metalloids,  produce  in  nitrobenzene  lowerings  which  always 
lie  between  67  and  73,  in  general  about  72. 
F  81 


MEMOIRS    ON 

The  alcohols  and  the  acids  (i.  e.,  the  hydroxyl  compounds) 
give  molecular  lowerings  in  nitrobenzene  between  35.5  and 
±2.2,  and  generally  about  36,  which  is  equal  to  half  the  preced- 
ing number. 

SOLUTION'S    IN   ETHYLEN"E   BROMIDE. 

The  ethylene  bromide  which  I  used  froze  at  7°.  92,  giving 
crystalline  opaque  plates  heavier  than  the  liquid.  Like  all  the 
other  solvents  which  can  be  frozen,  it  always  undergoes  under- 
cooling, but  to  a  less  extent.  Its  solvent  power  is,  as  it  ap- 
peared to  me,  exactly  analogous  to  that  of  benzene  and  chloro- 
form. It  undergoes  a  slow  change,  which  in  two  or  three  days 
lowers  its  freezing-point  to  an  appreciable  extent.  The  solu- 
tions ought,  therefore,  to  be  always  made  just  before  they  are 
used.  I  limited  myself  to  proving  by  some  experiments  that 
the  laws  observed  in  the  preceding  cases  are  applicable  here. 
The  following  results  were  obtained  : 

TABLE  V. 

SUBSTANCES   DISSOLVED  MOLECULAR 

IN   ETHYLENE  BROMIDE.  FORMULAS.  LOWEHING8. 

_/  —  At  A . 

Carbon  bisulphide ,...,,..    CS2  116.6 

Chloroform CH  C13  118.4 

Benzene O6H6  119.2 

Ether C\ffwO  117.5 

Arsenic  trichloride , As  C13  118.1 

ABNORMAL 
LOWERINGS. 

Aceticacid C2H^02  57.7 

Alcohol C2H60  56.8 

Therefore  : 

1.  There  is  a  maximum   of  molecular  lowering  in  ethylene 
bromide,  which  is  approximately  119. 

2.  The  molecular  lowerings  produced  by  different  compounds 
in  this  solvent,  approach  the  two  values  118  and  58,  the  one  being 
double  the  other;  a  result  similar  to  those  which  we  have  ob- 
served with  all  the  preceding  solvents. 


THE  MODERN  THEORY  OF  SOLUTION 


AQUEOUS  SOLUTIONS. 

As  I  have  observed  elsewhere,  water  is  the  only  solvent 
which  was  employed  by  my  predecessors,  and  the  metallic 
salts  the  only  substances  which  were  dissolved  in  it.  The  re- 
sults obtained,  although  numerous  and  remarkable,  especially 
from  the  point  of  view  of  the  existence  of  saline  hydrates  in 
the  solutions,  do  not  admit  of  general  conclusions.  It  is  right 
to  recall,  however,  that  De  Coppet  has  recognized  that  the  salts 
of  the  same  chemical  constitution  have  nearly  the  same  molecular 
lowering  ;  an  important  result  which  is  the  first  clew  to  the  great 
law  to  which  the  phenomenon  conforms.  (Ann.  Chim.  Phys., 
[4],  25.)  After  this  remark  De  Coppet  divided  salts  into 
five  groups,  as  follows,  having  nearly  the  same  molecular  low- 
ering : 

MOLECULAK 
LOWE1UNGS. 

(1)  Chlorides  and  hydrates  of  potassium  and  sodium.   34 

(2)  Chlorides  of  barium  and  of  strontium 45 

(3)  Nitrates  of  potassium,  sodium,  and  ammonium. . .   27 

(4)  Chromate,  sulphate,  carbonate  of  potassium;  sul- 

phate of  ammonium 38 

(5)  Sulphates  of  zinc,  magnesium,  iron,  copper 17 

The  results  pertaining  to  salts  in  aqueous  solution  present, 
therefore,  a  peculiar  complication,  which  we  have  not  met  with 
in  the  other  solvents.  However,  the  lowerings  produced  in  wa- 
ter appear  discordant  only  when  they  are  examined  closely  and 
separately.  As  soon  as  we  consider  all  of  the  effects  produced, 
not  only  by  the  salts  (which  behave  in  a  very  special  manner), 
but  also  by  the  soluble  oxides,  by  the  mineral  acids,  and 
especially  by  the  organic  substances,  we  recognize  also  here 
the  manifestation  of  the  general  law.  This  will  be  seen  from 
the  following  table.  I  have  not  introduced  the  salts  of  the 
metals  whose  atomicity  is  greater  than  2,  because  they  all  ap- 
pear to  undergo  more  or  less  decomposition  in  water : 


MEMOIRS    ON 

TABLE  VI. 

Lowering  of  the  Freezing  -Point  of  Aqueous  Solutions. 


IN  .  _ 

Hydrochloric  acid  .  ,  .  .......  .  .  .   //  Cl  39.1 

Hydrobromic  acid  .....  ....  ----   H  Br  39.6 

Nitric  acid  ...................  H  N03  35.8 

Perchloric  acid  ........  .......   H  Cl  <94  38.7 

Arsenic  acid  (?)  ...............  H3  As  04  42.6 

Phosphoric  acid  .....  ....  .....   ff3  P04  42.9 

Sulphuric  acid  ----  .  .  ..........   H2  S0±  38.2 

Selenious  acid  .............  .  .  .   Se  02  42.9 

Hydrofluosilicic  acid  .  .  ........   H2  SiFQ  46.6 

Potassium  hydrate  ......  ,,....   KOH  35.3 

Sodium  hydrate  ...............   Na  OH  36.2 

Lithium  hydrate  ..............   Li  OH  37.4 

Potassium  chloride  ............   K  Cl  33.6 

Sodium  chloride  ..............   Na  Cl  35.1 

Lithium  chloride  ..............   Li  Cl  36.8 

Ammonium  chloride  .  .  .  .  .......   NH4  Cl  34.8 

Potassium  iodide  ..............   KI  35.2 

Potassium  bromide  ............   K  Br  35.1 

Potassium  cyanide  .............   K  CN  32.2 

Potassium  ferrocyanide  ........    K±Fe  (CN)6  46.3 

Potassium  ferricyanide  ........   K^Fe  (CN)6  47.3 

Sodium  nitroprussiate  .........   Na  Fe(CN)5NO  46.8 

Potassium  sulphocyanate  .  .  .  ----   K  CNS  33.2 

Potassium  nitrate  .............   K  N0%  30.8 

Sodium  nitrate  ...............   Na  N03  34.0 

Ammonium  nitrate  ............  Nff4  N03  32.0 

Potassium  formate  ............  K  C  H  02  35.2 

Potassium  acetate  .............   K  C2  H3  02  34.  5 

Sodium  acetate  ...............   Na  C2  H3  02  32.0 

Potassium  carbonate  ...........   K2  C03  41.8 

Sodium  carbonate  .............   Naz  CO^  40.3 

Potassium  sulphate  ............   K2  S0±  39.0 

Acid  potassium  sulphate  .......   KHSO±  34.8 

Sodium  sulphate  ..............   Na2  S04  35.4 

Ammonium  sulphate  ..........    (NH±}2  S04  37.0 

84 


THE    MODERN    THEORY    OF    SOLUTION 


SUBSTANCES    DISSOLVED 
IN  WATER. 


TAIJLE  VI. — (Continued.} 

FORMULAS. 


MOLECULAR 
LOWERING  S. 


Sodium  tetraborate  (borax)  ....  Xa2B4  07  66.0 

Potassium  chromate  ...........  K2  Or  0±  38.1 

Potassium  bichromate  .....  ....  K2  Cr2  0T  43.7 

Disodium  phosphate   ..........  Xa2  H  PO^  37.9 

Sodium  pyrophosphate  ........  Xa4  P2  0-  45.8 

Potassium  oxalate  .............  K2C20±  46.8 

Sodium  oxalate  ...............  Xa2  C2  04  43.2 

Potassium  tartrate  ............  K2C\H±  06  36.3 

Sodium  tartrate  ...............  Xa2  C\  H±  06  44.2 

Acid  sodium  tartrate  ..........  XaH  C\  H4  06  31.2 

Barium  hydroxide  .............  Ba(OH)2  49.7 

Strontium  hydroxide  ..........  Sr(OH)2  48.2 

Calcium  hydroxide  ............  Ca  (OH)2  48.0 

Barium  chloride  ..............  Ba  C12  48.6 

Strontium  chloride  ............  Sr  CI2  51.1 

Calcium  chloride  ..............  CaCl2  49.9 

Cupric  chloride  ...............  Cu  CI2  47.8 

Barium  nitrate  ................  Ba  (X03)2  40.5 

Strontium  nitrate  .............  Sr  (X03)2  41.2 

Calcium  nitrate  ...............  Ca  (X03}2  37.4 

Lead  nitrate  ..................  Pl>  (NO^)2  37.4 

Barium  formate  ...............  BaC2H20^  48.2 

Barium  acetate  ...............  BaC^H^O^  48.0 

Magnesium  acetate  ............  Mg  C4  H6  0±  47.8 

ABNORMAL 
LOWERINGS. 

Sulphurous  acid  ..............  S02  20.0 

Hydrogen  sulphide  ........  ____  H2  S  19.2 

Arsenious  acid  ................  H3  As  03  20.3 

Metaphosphoric  (?)  acid  .......  HP  03  21.7 

Boric  acid  ....................  H3  B03  20.5 

Potassium  antimonyl  tartrate.  ..  KSbG\H.fOt  18.4 

Mercuric  cyanide  ..............  Hg  (CX)2  17.5 

Magnesium  sulphate  ...........  Mg  80^  19.2 

Ferrous  sulphate  ..............  Fe  S0±  18.4 

Zinc  sulphate  ........  .........  Zn  S04  18.2 

Copper  sulphate..  .............  CuSO^  18.0 

85 


MEMOIRS    ON 

TABLE  VI.  —  (Concluded.) 
Organic  Compounds* 


T=MA. 

Methyl  alcohol  .....  •  ...........    CII.O  17.3 

Ethyl  alcohol  .................    C2  H6  O  17.3 

Butyl  alcohol  .................    O4HWO  17.2 

Glycerin  .....................    C3ff803  17.1 

Mannite  ......................    O6HUO6  18.0 

Dextrose  .....................    C6H1206  19.3 

Milk  sugar  ...................    C12  H22  Ou  18.1 

Salicin  .......................    6'13//18  0,  17.2 

Phenol  .......................    C6H60  15.5 

Pyrogallol  ....................    O6H6O,  16.3 

Chloral  hydrate  ...............    C2C13H302  18.9 

Acetone  ......................    O3H6O  17.1 

Formic  acid  ..................   H,C02  19.3 

Acetic  acid  ...................    C2ff^02  19.0 

Butyric  acid  ..................    O,HQO2  18.7 

Oxalic  acid.  .  .  ................    CZH20  22.9 

Lactic  acid  ...................    C3H6  OL  19.2 

Malic  acid  .  .  .  .  ................    C\H605  18.7 

Tartaric  acid  .................    QH606  19.5 

Citric  acid  ....................    CGHQ0~,  19.3 

Ether  ........................    C4H}0O  16.6 

Ethyl  acetate  .................    V4H802  17.8 

Hydrocyanic  acid  .............   H  CN  19.4 

Acetamide  ...................    C2H5NO  17.8 

Urea  ..........................    CON2H,  17.2 

Ammonia  .....................  A7/T3  19.9 

Ethylamine  ..................    C2  NH7  18.5 

Propylamine  ..................    C3  NH9  18.4 

Aniline  ......................    C6  NH7  15.3 

Notwithstanding  the  variations  which  are  much  larger  than 
with  the  other  solvents,  we  find  here  also  the  laws  previously 
observed. 

*  [This  table  is  taken  from  Ann.  Cliim.  Pliys.,  (5),  28,  137  (1883).] 

86 


THE    MODERN    THEORY    OF    SOLUTION 

For  the  compounds  which  are  not  dissociated  in  water  there  is 
a  maximum  of  the  molecular  lowering,  which  is  about  47.* 

The  molecular  lowerings  of  some  salts  which  are  not  decom- 
posable by  water  are,  it  is  true,  larger  than  this  value.  But 
this  arises,  in  a  great  measure,  from  the  fact  that  they  are 
referred  to  substances  which  we  suppose  to  be  anhydrous, 
while  these  really  exist  as  hydrates  in  the  solutions.  As  an 
example,  the  molecular  lowering  of  barium  chloride  is  48.6 
when  we  suppose  this  salt  to  be  anhydrous  in  the  solutions, 
but  falls  to  46.9  when  we  suppose  it  to  exist  in  the  solutions  as 
the  hydrate  Ba  C724-2  H2  O,  as  Rlidorff  thinks  it  does.  Some 
deviations  ought  also  to  be  attributed  to  impurities. 

Two  compounds  are  exceptions  to  this  law,  if  we  adopt  for 
them  molecular  weights  which  are  double  the  equivalents,  as 
most  modern  chemists  are  inclined  to  do.  These  are  :  potas- 
sium ferricyanide  and  sodium  nitroprussiate.  As  a  matter  of 
fact,  with  the  formulas  K6Fe2(CN)l2  and  Na4(NO)2Fe2(C^V)lQ 
we  find  for  the  molecular  lowering  of  each  of  these  sub- 
stances a  value  which  is  exactly  double  the  maximum,  47. 
But  these  formulas  do  not  appear  to  be  necessary  for  the 
explanation  of  the  chemical  properties  of  these  substances,  and 
nothing  is  opposed,  as  far  as  I  know,  to  assigning  to  them, 
at  least  in  solution,  the  formulas  K-^Fe  (CN)6  and  Na2  NO- 
Fe  (CN)5,  which  correspond  to  the  maximum  molecular  lower- 
ing. The  only  serious  objection  resulting  from  the  formula 
/i"3  Fe  ((Ly)6  is  that  potassium  ferricyanide  appears  to  be  a  sub- 
stance containing  an  odd  number  of  unsaturated  bonds.  But 
this  anomaly  is  found  in  some  other  compounds — e.  g.,  in  alu- 
minium ethyl — and  it  alone  is  not  a  sufficient  reason  for  con- 
demning a  formula  which  agrees  so  well  with  the  physical  facts. 
I  have,  therefore,  adopted  for  these  substances  molecular 
weights  equal  to  the  equivalents. 

A  glance  at  the  figures  in  the  last  column  of  the  preceding 
table  shows  that  the  molecular  lowerings  of  the  freezing-point  of 
icater  are  grouped  around  the  two  numbers  37  and  18.5,  the  one 
being  double  the  other;  so  that  the  law  observed  with  acetic 

*  Borax,  which  decomposes  in  water,  as  Berthelot  has  shown  (Median. 
Chim.,  II.,  224),  appears  in  the  table  with  a  molecular  lowering  of  66.  But 
this  number  is,  in  reality,  the  sum  of  the  molecular  lowerings  of  the  acid 
and  base  into  which  the  original  salt  decomposes,  and  each  of  these  ap- 
pears in  the  law  enunciated. 

87 


MEMOIRS    ON 

acid,  formic  acid,  benzene,  nitrobenzene,  and  ethylene  bromide, 
still  manifests  itself,  although  less  clearty,  when  water  is  used 
as  a  solvent. 

One  fact  shows  clearly  the  simple  relation  which  exists,  even 
in  water,  between  the  normal  and  abnormal  lowerings.  The 
solution  of  anhydrous  phosphoric  acid  in  water,  made  in  the 
cold,  has,  for  more  than  an  hour,  a  molecular  lowering  of  21.7. 
If  it  is  boiled  and  the  liquid  brought  to  the  original  volume  by 
adding  water,  we  find  that  the  molecular  lowering  is  about 
44.2,  that  is,  it  is  doubled. 

The  molecular  lowerings  of  all  the  salts  of  the  alkalies  and 
alkaline  earths,  of  all  the  strong  acids  and  bases,  are  grouped 
around  the  mean  normal  lowering  37.  The  abnormal  molec- 
ular lowering  18.5  belongs  to  some  salts  of  the  bivalent  metals, 
to  all  the  weak  acids  and  bases,  and,  without  exception,  to  all 
of  the  organic  compounds  which  are  non-saline. 

CONCLUSIONS. 

Several  important  propositions  follow  from  the  mass  of  facts 
recorded  in  this  paper: 

1.  Every  substance,  solid,  liquid,  or  gaseous,  when  dissolved 
in  a  definite  liquid  compound  capable  of  solidifying,  lowers  its 
freezing-point.  This  fact,  which  it  was  impossible  to  foresee, 
and  of  which  it  will  be  very  interesting  to  know  the  cause,  is  ab- 
solutely general.  The  exceptions  which  arc  observed  are  only 
apparent  and  are  easily  explained.  Thus,  when  we  dissolve 
anhydrous  stannic  chloride  in  acetic  acid  containing  a  little 
water,  each  molecule  of  the  chloride  combines  with  two  mole- 
cules of  water  forming  only  one  molecule  of  the  hydrate.  In- 
stead of  two  molecules  in  solution,  there  is,  therefore,  only  one, 
and  an  elevation  of  the  freezing-point  necessarily  results ;  for, 
as  we  shall  see  later,  the  amount  of  lowering  depends  only  upon 
the  relation  between  tlie  number  of  molecules  of  the  dissolved 
substance  and  of  the  solvent. 

But  such  an  effect  is  due  entirely  to  the  reciprocal  action  of 
the  dissolved  substances.  It  is  never  produced  when  the  solv- 
ent is  a  definite  compound,  free  from  impurities.  It  results 
lfrom  the  above  principle  that :  of  two  specimens  of  a  substance, 
that  one  is  purer  which  solidifies  or  melts  at  the  higher  tem- 
perature. 

88 


THE  MODERN  THEORY  OF  SOLUTION 

This  furnishes  an  excellent  means,  unfortunately  limited  in 
its  applicability,  of  examining  the  purity  of  substances. 

2.  There  is  in  each  solvent  a  maximum  molecular  lowering  of 
the  freezing-point.     This  maximum  lowering  is  about  47  in 
water,  36  in  acetic  acid,  29  in  formic  acid,  50  in  benzene,  73  in 
nitrobenzene,  119  in  ethylene  bromide. 

This  fact  can  be  applied  directly  to  the  determination  of  a 
certain  number  of  molecular  weights.  Given  a  compound  whose 
molecular  weight  it  is  desired  to  know  ;  we  determine  its  co- 
efficient of  lowering,  A,  in  one  of  the.  preceding  solvents,  then 
divide  the  maximum  molecular  lowering  of  the  solvent  em- 
ployed by  A,  and  we  obtain  the  maximum  of  the  molecular 
weight.  We  know,  besides,  that  the  molecular  weight  corre- 
sponds to  the  simplest  atomic  formula  of  the  compound  ex- 
amined, or  to  a  whole  multiple  of  this  formula.  Whenever, 
then,  the  maximum  found  is  not  twice  the  molecular  weight 
corresponding  to  the  simplest  atomic  formula,  the  latter  ought 
to  be  adopted. 

3.  The  molecular  lowerings  of  the  freezing-point  of  all  the 
solvents,  produced  by  the  different  confounds  dissolved  in  them, 
approach  two  mean  values,  wliicli  vary  with  the  nature  of  the  solv- 
ent, the  one  being  twice  the  other.     These  mean  values  are  117 
and  58  for  ethylene  bromide,  72  and  36  for  nitrobenzene,  49 
and  24  for  benzene,  39  and  19  for  acetic  acid,  28  and  14  for 
formic  acid,  37  and  18.5  for  water.     The  larger  of  the  two 
lowerings,  which  I  call  normal  lowering,  is  produced  much  more 
frequently  than  the  smaller,  and  in  all  the  solvents  studied, 
with  the  exception  of  water,  it  is  obviously  identical  with  the 
maximum  molecular  lowering.     In  formic  and  acetic  acids  it 
appears   almost   constantly.      In   benzene,    nitrobenzene,    and 
ethylene  bromide,  it  is  produced  by  all  substances  which  do 
not  contain  hydroxyl,  and  consequently  by  all  substances  which 
have  a  constitution  analogous  to  that  of  the  solvents.     In  water 
it  is  produced  by  the  strong  acids,  and  by  the  salts  whose  acid 
or  base  is  monatomic. 

The  substances  which  produce  normal  or  abnormal  lowering 
in  a  given  solvent  belong  to  well-defined  groups,  and  this  fact 
can  also  be  utilized  for  the  determination  of  MOLECULAR 
WEIGHTS.  All  the  salts  of  the  alkalies  in  solution  in  water 
give  a  molecular  lowering  which  is  approximately  37.  If,  then, 
we  have  to  choose  between  several  numbers  which  are  multiples 


MEMOIRS    ON 

of  one  another,  for  the  molecular  weight  of  a  salt  of  an  alkali, 
we  choose  that  one  which,  multiplied  by  the  coefficient  of 
lowering  of  the  salt  in  water,  gives  the  number  nearest  to  37. 
Similarly,  with  respect  to  the  organic  substances  soluble  in 
water,  that  molecular  weight  is  to  be  adopted  which,  multi- 
plied by  the  coefficient  of  lowering  in  water,  gives  the  num- 
ber nearest  to  18.5  (Ann.  Chim.  Phys.,  January,  1883).  All 
organic  substances  in  solution  in  acetic  acid  give  a  molecular 
lowering  of  about  39.  The  formula  which  must  be  adopted  for 
an  organic  compound  soluble  in  this  solvent  is,  then,  that 
which  corresponds  to  the  molecular  weight  the  closest  to  the 
number  obtained  by  dividing  39  by  the  coefficient  of  lowering 
of  this  substance  in  acetic  acid.  As  most  of  the  compounds 
are  soluble  either  in  water  or  in  acetic  acid,  this  method  fur- 
nishes the  means  of  establishing  the  molecular  weights  in  a  large 
number  of  cases.  If  necessary,  the  coefficients  of  lowering  in 
benzene,  or  in  other  solvents,  can  be  turned  to  account.  There 
are,  then,  but  few  compounds,  whatever  their  nature,  whose 
molecular  weight  cannot  be  established  by  the  method  of  freez- 
ing the  solvents.  But  I  must  not  enlarge  further  upon  this 
subject  here,  and  shall  return  to  it  in  a  special  work.  It  suf- 
fices to  have  indicated  this  important  application. 

Returning  to  the  experimental  facts  already  stated,  we  can 
explain  them  by  admitting  that :  In  a  constant  weight  of  a  given 
solvent,  all  the  physical  molecules,  whatever  their  nature,  produce 
the  same  lowering  of  the  freezing-point.  According  to  this  hypoth- 
esis, when  the  dissolved  substances  are  completely  disintegrated, 
as  they  would  be  in  a  perfect  vapor,  and  when  each  physical 
molecule  contains  only  one  chemical  molecule,  the  molecular 
lowering  is  a  maximum,  and  the  same  for  all.  When  the  chemi- 
cal molecules  are  united  in  pairs,  to  a  greater  or  less  extent,  form- 
ing a  certain  number  of  double  physical  molecules,  the  lowering 
produced  is  less  than  if  the  condensation  had  not  taken  place, 
since  each  of  these  double  molecules  produces  the  same  effect 
as  one  simple  molecule.  If  all  of  the  chemical  molecules 
are  united  in  pairs,  the  lowering  is  half  the  maximum.  The 
abnormal  lowerings  in  almost  all  of  the  solvents  correspond  to 
this  condition.  When  water  is  employed  as  solvent,  we  observe 

certain  number  of  abnormal  lowerings,  which  are  considerably 
less  than  half  the  maximum  lowering.  This  shows  that  the 
condensation  can  proceed  still  further.  The  exceptionally  small 

90 


THE    MODERN    THEORY 

lowering  of  phenol  and  pyrogollol  in  water  can  be  explained  by 
assuming  that  the  molecules  of  these  substances  are  united  in 
groups  of  three.  To  explain  all  of  the  facts  observed,  it  there- 
fore suffices  to  apply  to  the  constitution  of  dissolved  substances 
the  hypotheses  admitted  by  all  for  the  constitution  of  vapors. 

The  preceding  considerations  explain  the  effects  produced 
by  different  compounds  in  a  given  solvent;  but  they  indicate 
nothing  as  to  the  value  of  the  lowering  produced  by  a  given 
compound  in  different  solvents. 

In  order  to  bring  out  the  law  relating  to  the  nature  of  the 
solvents,  it  is  necessary  to  reduce  the  .results  by  calculation 
to  the  case  of  1  molecule  of  each  substance  dissolved  in  100 
molecules  of  the  solvent  This  is  accomplished  by  dividing 
the  molecular  lowering  of  each  substance,  T,  by  the  molecular 
weight  of  the  solvent,  M'.  Indeed,  the  molecular  lowerings 
are  those  produced  by  1  molecule  of  a  foreign  substance  in  100 

i  <  K  ) 

grams,  or  iuj  -^-,  molecules  of  the  solvent.     Moreover,  from  the 
'  Jj±  • 

law  of  Bla^en,  the  lowerings  are,  ceteris  paribus,  inversely 
proportional  to  the  quantities  of  solvent  which  contain  1.  mole- 
cule dissolved  in  them.  We  have  then,  calling  T'  the  lowering 
produced  by  1  molecule  dissolved  in  100  molecules  : 


from  which  :  77 

T'  __      . 
~M' 

If,  then,  we  divide  the  molecular  lowerings  indicated  above  by 
the  molecular  weights  of  the  solvents  to  which  they  refer,  we 
reduce  the  results  to  the  case  of  1  molecule  of  the  dissolved 
substance  in  100  molecules  of  the  solvent.  Below  are  the  re- 
sults obtained  by  introducing  into  the  calculation  the  values 
of  7*  corresponding  to  a  maximum  molecular  lowering  : 

Maximum  Molecular  Lower- 

Molecular  Maximum  Molecular     ing  Divided  by  the  Molec- 

Weights  towering    Produced     ular  Weight  of  the  Solvent, 

Solventa  of  by  1  Molecule  iu  100     or  Lowering  Produced  by  1 

Solvents.  Grams.  Molecule  in  100  Molecules. 

Water  ..........  18  47  2°.61 

Formic  acid  .....  46  29  0°.63 

Acetic  acid  ......  60  39  0°.6o 

Benzene  .........  -  78  50  0°.64 

Nitrobenzene  ----  123  73  0°.59 

Ethylene  bromide  188  119  0°.63 

91 


MEMOIRS    ON 

Leaving  out  of  the  question  for  the  moment  water,  which  be- 
haves in  a  peculiar  manner,  we  see  that  the  maximum  lowering 
of  the  freezing-point,  which  results  from  the  action  of  1  mole- 
cule dissolved  in  100  molecules  of  solvents,  varies  only  from 
0°.59  to  0°.65,  mean  0°.63,  and  is  consequently  nearly  the  same 
in  all  of  the  solvents.  This  fact  is  the  more  remarkable  since 
the  molecular  lowerings  which  enter  into  the  calculation  vary 
considerably — namely,  in  the  ratio  of  1  to  4.  It  is,  moreover, 
reasonable.  In  fact,  whatever  is  the  nature  of  the  action  ex- 
erted between  the  molecules  of  the  solvent  and  those  of  the 
dissolved  substance,  it  seems  that  it  ought  to  be  mutual ;  and 
if  the  effect  is  independent  of  the  nature  of  the  dissolved  sub- 
stance, it  ought  probably  to  be  independent  also  of  the  nature 
of  the  solvent. 

Water  is  the  only  exception  ;  but  it  is  not  astonishing  on  the 
part  of  a  liquid  which  presents  so  many  other  peculiarities.  To 
explain  the  anomaly,  it  is  allowable  to  suppose  that  each  of  the 
physical  molecules  of  which  water  is  composed,  is  formed  of 
several  chemical  molecules  united  with  one  another.  At  the 
time  when  I  had  found  only  a  few  molecular  lowerings  in 
aqueous  solutions  larger  than  the  mean  lowering  37,  I  believed 
that  the  physical  molecules  of  water  were  formed  of  3  chemical 
molecules.  Indeed,  by  dividing  37  by  18x3,  we  obtain  0.685, 
which  is  not  very  far  removed  from  the  mean  value  0.63  obtained 
with  other  solvents.  This  I  have  observed  in  a  previous  pub- 
lication {Compt.  rend.,  November  27th,  1882).  But,  in  the 
light  of  new  determinations,  it  is  no  longer  possible  to  consider 
as  doubtful  the  molecular  lowerings  which  are  much  larger 
than  37,  and  I  am  compelled  to  recognize  that  the  molecular 
lowerings  in  water  can  be  even  as  great  as  47,  a  maximum 
value  in  most  cases  where  the  dissolved  substances  do  not 
decompose.  Such  a  lowering  can  be  explained  by  admitting 
that  the  molecules  of  water  are  united  in  groups  of  four,  at  least 
in  the  neighborhood  of  zero.  Then,  indeed,  47  divided  by 
18x4  is  0.65,  which  is  remarkably  near  the  mean  0.63  obtained 
with  other  solvents. 

The  anomalies  relating  to  solvents,  like  those  relating  to  dis- 
solved substances,  can  then  be  explained  by  the  condensation 
of  the  molecules,  and  they  do  not  prevent  us  from  expressing 

the  GENERAL  LAW  OF  THE  FREEZING  OF  SOLVENTS,  as  follows  : 

molecule  of  any  substance,  is  dissolved  in  100  molecules  of 
92 


THE    MODERN    THEORY    OF    SOLUTION 

any  liquid  of  a  different  nature,  the  lowering  of  the  freezing- 
point  of  this  liquid  is  always  nearly  the  same,  and  approxi- 
mately 0°.G3. 

Consequently,  the  lowering  of  the  freezing-point  of  a  dilute 
solution  of  any  strength  whatever  is,  obviously,  equal  to  the  prod- 
uct obtained  by  multiplying  63  by  the  ratio  between  the  number 
of  molecules  of  the  dissolved  substance  and  that  of  the  solvent. 

Let  us  recall,  iu  conclusion,  that  the  molecules  with  which 
we  are  here  dealing  are  physical  molecules,  which,  in  certain 
cases,  can  be  formed  by  two  or  several  chemical  molecules 
united  with  one  another. 


r 


.*  , 

^ 


V 


<* 


A/  ._ 

/    I  \t 

'  ^ 


AW  IV 

<& 

UNIVERSITT 


ON  THE  VAPOR-PRESSURE  OF  ETHEREAL 
SOLUTIONS 

BY 

F.    M.    RAOULT 

Professor  of  Chemistry  in  Grenoble 
(Annales  de  Chimie  et  de  Physique,  [6],  15,  375, 1888) 


CONTENTS 

PACK 

Method  of  Work 97 

Influence  of  Concentration  on  the  Vapor- Pressure  of  Ethereal  Solutions.  105 

General  Results 110 

Laws  Pertaining  to  Dilute  Solutions 112 

Particular  Expression  of  the  Law  Pertaining  to  Dilute  Solutions 113 

Influence  of  Temperature  on  the  Vapor- Pressure  of  Ethereal  Solutions. .  114 
Influence  of  the  Nature  of  the  Dissolved  Substance  on  the  Vapor- Pressure 

of  Ethereal  Solutions 116 

Another  Expression  of  the  Law 119 


ON  THE  VAPOR-PRESSURE  OF  ETHEREAL 
SOLUTIONS* 

BY 

F.    M.   RAOULT 

I  DISCOVERED  some  time  ago  (Compt.  rend.,  July  22, 1878)  that 
a  close  relation  exists  between  the  lowering  of  the  vapor-press- 
ures of  aqueous  solutions,  the  lowering  of  their  freezing-points, 
and  the  molecular  weights  of  the  dissolved  substances.  This 
observation  was  the  starting-point  for  my  researches  on  the 
freezing-point  of  solutions  (Compt.  rend.,  94  to  1O1),  and  it 
is  this  which  now  leads  me  to  undertake  a  similar  piece  of 
work  on  their  vapor-pressures. 

I  employed,  first,  ethereal  solutions,  since  they  lend  them- 
selves easily  to  this  kind  of  study.  To  simplify  the  question 
I  shall  consider  here  only  the  case  where  the  vapor-pressure  of 
the  dissolved  substances  is  very  small,  and  is  negligible  with 
respect  to  that  of  the  ether.  In  a  subsequent  investigation  I 
shall  examine  the  more  general  case,  where  the  dissolved  sub- 
stances themselves  have  a  considerable  vapor-pressure. 

I  determined  the  vapor-pressures  of  these  kinds  of  solutions 
by  the  method  of  Dalton.  I  measured  with  the  cathetometer 
the  heights  to  which  the  mercury  is  raised  in  the  barometric 
tubes,  the  one  containing  only  mercury,  the  other,  in  addition, 
a  small  quantity  either  of  pure  ether  or  of  ether  in  which  were 
dissolved  different  substances  which  are  nearly  non-volatile. 
Before  making  the  measurements  I  shook  all  of  the  solutions, 
moistening  well  the  walls,  and  not  until  ten  minutes  later  did 
I  proceed  with  the  measurements,  the  temperature  remaining 
constant.  In  the  calculation  of  the  results  I  have  taken  care 
to  add  to  the  pressure  of  the  mercury  in  each  tube  the  pressure 

*  Ann.  Chim.  Phys.,  [6],  15,  375  (1888) ;  Ztschr.  Phys.  Chem.,  2,  353(1888). 
G  97 


MEMOIRS    ON 

which  arises  from  the  small  column  of  ether,  or  of  ethereal 
solution,  which  is  placed  upon  it.  I  have  even  taken  the  pre- 
caution to  correct  the  concentration  of  the  solutions  for  the 
small  quantity  of  ether  separated  as  vapor. 

The  quantities  upon  which  all  of  the  comparisons  are  based, 
and  which  are  to  be  determined,  are  :  the  vapor-pressure  of  the 
pure  ether,/,  and  the  vapor -pressure  of  the  ether  containing 
the  dissolved  substance,  /',  the  temperature  remaining  the 
same.  To  determine  these  quantities  as  accurately  as  possi- 
ble, I  worked  as  follows  : 

Preparation  of  the  Ether. — Pure  commercial  ether  was  taken, 
and  after  washing  it  with  water  it  was  shaken  several  times 
with  a  concentrated  aqueous  solution  of  caustic  potash.  It 
was  digested  over  calcium  chloride  and  distilled  in  a  Le  Bel 
and  Henninger  apparatus  with  eight  bulbs.  The  portion 
which  distils  at  a  constant  temperature  was  left  in  contact  with 
thin  fragments  of  sodium  for  forty-eight  hours,  in  a  balloon 
flask  provided  with  a  condenser  with  eight  bulbs.  It  was  then 
distilled  a  second  time.  Nearly  all  of  it  distilled  at  34°. 7  under 
760  millimetres  pressure.  Regnault  gave  34°.  97  as  the  boiling- 
point  of  ether. 

Regnault  says  that  he  had  considerable  trouble  in  obtaining 
an  ether  which  was  always  exactly  the  same.  He  observed  this 
substance  undergo  change  by  prolonged  boiling  under  slight 
pressure.  He  observed  it  undergo  change  even  at  the  ordi- 
nary temperature,  in  a  flask  hermetically  closed  and  freed 
from  air.  The  change  was  manifested  only  by  a  change  in 
the  vapor -pressure  (Mem.  de  I'Acad.  des  Sciences,  26,  1862). 
Perhaps  this  change  resulted  from  the  fact  that  the  ether 
used  by  Regnault,  which  had  not  been  distilled  from  sodium, 
contained  traces  of  water  or  of  ethyl  peroxide.  Lieben  (Ann. 
CJiem.  Pharm.,  165)  was  not  able  to  prove  the  presence  of  any 
trace  of  alcohol,  even  after  a  year,  in  ether  distilled  from  sodium 
and  preserved  in  a  closed  vessel.  For  my  part,  I  found  that 
pure  ether,  preserved  for  five  months  in  a  barometric  tube  at 
ordinary  temperatures,  had,  at  15°,  exactly  the  same  vapor- 
pressure  as  at  the  beginning.  It  is  not  certain  but  that  ether, 
even  when  very  pure,  undergoes  a  more  or  less  rapid  change  in 
the  flasks  in  which  it  is  preserved,  and  into  which  the  air  always 
penetrates  a  little.  This  lowers  its  vapor-pressure  and  gives  it 
the  property  of  soiling  mercury.  It  is,  therefore,  necessary  to 


THE  MODERN  THEORY  OF  SOLUTION 

use  it  immediately  after  it  has  been  distilled  from  sodium.  I 
have  always  done  this.  I  do  not,  however,  think  that  the 
ether  which  I  employed  was  absolutely  pure.  It  contained, 
indeed,  a  small  quantity  of  a  gas  which  appeared  to  me  to  be 
a  hydrocarbon,  and  from  which  I  never  succeeded  in  completely 
freeing  it.  This  compelled  me  to  employ  very  long  tubes,  as 
will  be  seen  later. 

Preparation  of  the  Solutions. — The  substances  which  I  dis- 
solved in  ether  were  chosen  from  those  whose  boiling-points  are 
above  160°,  and  their  vapor-pressure  at  the  ordinary  tempera- 
ture was  scarcely  6  millimetres  of  mercury.  It  is  therefore 
a  simple  matter  to  work  with  them.  To  make  solutions  of 
known  strength,  a  certain  quantity  of  the  substance  is  weighed 
in  flasks  of  20  centimetres  capacity,  provided  with  good  corks. 
A  sufficient  quantity  of  ether  is  then  poured  into  each  of  these 
flasks,  which  are  now  closed  and  reweighed.  The  increase  in 
weight  is  the  weight  of  the  ether.  In  preparing  dilute  solu- 
tions— i.  e.,  solutions  containing  only  a  small  quantity  of  non- 
volatile substance — this  is  weighed  in  thin-walled  bulbs,  which 
are  afterwards  broken  by  shaking  in  the  flasks  containing  a 
known  quantity  of  ether,  which  is  large  with  respect  to  the 
amount  of  substance. 

Choice  of  Barometric  Tubes. — I  employ  tubes  of  colorless 
glass,  and  of  about  1  centimetre  internal  diameter.  The  capil- 
lary effect  in  such  tubes  is  not  zero,  but  we  endeavor  to  make  it 
constant  throughout  the  entire  length  of  the  tube  by  choosing 
the  tubes  as  nearly  cylindrical  as  possible.  This  does  not  pre- 
vent the  determination  of  its  exact  value  and  correcting  the  re- 
sults accordingly,  as  we  will  see  later.  After  having  cleansed 
and  dried  the  interior  of  the  tubes,  they  are  drawn  out  at  90 
centimetres  from  the  end  to  a  long  tube,  which  is  bent  about 
the  middle  in  the  form  of  a  hook.  An  elliptic  ring  of  not 
very  stout  platinum  wire  is  shoved  clear  up  to  the  top  of  each 
of  these,  and  remains  there  by  virtue  of  its  elasticity.  This  is 
used  to  stir  the  interior  liquid. 

Filling  the  Tubes. — To  fill  one  of  these  tubes  it  is  thrust  into 
a  deep  mercury  bath,  the  drawn-out  end  being  kept  above  the 
bath.  When  it  is  almost  entirely  immersed  in  the  mercury, 
the  descending  limb  of  the  bent  tube  is  inserted  in  a  small  flask 
containing  the  ethereal  solution  which  it  is  desired  to  introduce 
into  the  tube.  The  tube  and  flask  are  carefully  raised  and  the 

99 


MEMOIRS    ON 


solution  is  quickly  drawn  into  the  tube.  When  this  liquid  has 
reached  a  depth  of  about  3  centimetres  in  the  cylindrical  por- 
tion of  the  tube,  the  flask  is  removed,  and  without  raising  the 
tube  farther  the  point  is  closed  with  a  burner  a  few  millimetres 
from  the  ethereal  solution.  It  is  now  necessary  to  expel  the 

gases  adhering  to  the  walls, 
or  dissolved  in  the  liquid, 
without  losing  any  trace  of 
ether  by  evaporation. 

To  accomplish  this  the 
barometric  tube  is  raised 
nearly  out  of  the  deep  bath, 
leaving  the  end  only  1  to 
2  centimetres  under  the 
mercury.  By  means  of  two 
hot  irons  placed  against  the 
tube  the  solution  is  boiled 
with  sufficient  rapidity,  and 
long  enough  to  drive  the 
mercury  down  to  the  bot- 
tom. The  heating  is  then 
discontinued,  and  the  tube 
again  thrust  into  the  deep 
bath.  When  the  mercury  in  the  interior  is  on  the  same  plane 
as  that  on  the  exterior,  the  end  of  the  fine  point  is  cut  off  with 
scissors,  and  then  the  tube  is  slowly  thrust  farther  into  the 
bath.  The  ethereal  solution  enters  the  capillary  portion,  and, 
when  it  is  only  a  few  millimetres  from  the  end,  this  is  closed 
with  a  blow-pipe.  The  same  operation  is  begun  again,  then  a 
third  time, when  there  remains  in  the  tube  only  a  trace  of  gas, 
which,  under  atmospheric  pressure,  generally  occupies  not  more 
than  3  to  4  millimetres.  The  influence  which  this  small  quan- 
tity of  gas  exerts  on  the  heights  of  the  mercurial  columns  is 
negligible  in  my  experiments.  Finally,  the  tube  thus  pre- 
pared was  removed  to  a  special  mercury  bath,  wide,  and  shal- 
low, where  it  could  be  observed. 

Arrangement  for  Stirring  the  Contents  of  the  Tubes. — In  the 
barometric  tubes  thus  prepared,  the  ethereal  solutions,  and 
ether  itself  if  not  absolutely  pure,  tend  constantly  to  lose 
their  homogeneity,  due  to  changes  in  temperature  and  to  the 
atmospheric  pressure.  If  the  volume  of  the  vapor  diminishes, 

100 


Fig.  i 


THE    MODERN    THEORY    OF    SOLUTION 

due  to  these  variations,  a  certain  quantity  of  ether  vapor  con- 
denses in  each  tube,  which  results  in  a  dilution  of  the  upper 
portions  of  the  liquid  layers  in  contact  with  the  vapor.  The 
opposite  effect  is  produced  if  the  volume  of  the  vapor  increases. 
If,  therefore,  care  is  not  taken,  the  vapor-pressures  observed  cor- 
respond to  solutions  whose  concentration  is  uncertain,  and  more 
or  less  different  from  that  of  the  original  liquids.  To  avoid  this 
source  of  error,  not  pointed  out  up  to  the  present,  I  have  always 
been  careful  to  shake  the  liquids  several  minutes  before  deter- 
mining their  vapor-pressure.  At  first  I  seized  each  tube  in  suc- 
cession with  wooden  forceps,  and  inclined  it  until  the  ether  came 
in  contact  with  the  top.  I  then  righted  it  again,  and  repeated 
this  several  times.  I  use  now  the  following  arrangement,  which 
gives  the  same  result  more  rapidly  and  more  conveniently : 

The  mercury  bath,  in  which  the  barometric  tubes  rest,  is  of 
cast-iron,  wide  and  shallow,  and  firmly  supported  on  a  column 
of  masonry.  On  its  upper  edge  is  a  screw-nut  in  which  a  screw 
10  centimetres  long  is  held  vertically,  its  lower  point  just 
touching  the  surface  of  the  mercury.  The  barometric  tubes, 
generally  six  in  number,  rest  upright  on  a  narrow  shelf  im- 
mersed in  the  mercury  of  the  bath,  and  which  forms  the  lower 
part  of  an  iron  frame,  to  which  they  are  fastened  by  iron  wire. 
The  frame  can  rock  with  all  the  tubes  which  it  carries,  turning 
on  its  base  as  a  hinge,  without  the  end  of  the  tubes  coming  out 
of  the  bath.  We  are  thus  able,  by  inclining  the  frame  and 
righting  it  several  times,  to  shake,  simultaneously,  the  solutions 
contained  in  all  the  tubes  which  it  carries,  and  to  wet  the  walls 
quite  up  to  the  top.  The  small  rings  of  platinum  wire,  which 
are  placed  up  in  the  top  of  the  tubes,  facilitate  the  stirring  very 
much.  The  tubes,  having  been  restored  to  the  vertical  position, 
are  left  to  rest  for  about  ten  minutes,  when  the  heights  are 
measured. 

The  necessity  of  agitation  can  be  easily  demonstrated  by 
experiment.  Two  tubes,  the  one  containing  pure  ether,  the 
other  an  ethereal  solution,  having  been  placed  side  by  side, 
are  not  disturbed  for  a  day  or  two.  The  difference  between 
the  heights  of  the  mercurial  columns  is  then  measured.  The 
tubes  are  then  shaken,  and  fifteen  minutes  after  the  shak- 
ing we  almost  always  find  considerable  increase  in  this  differ- 
ence, even  when  the  temperature  has  remained  absolutely  the 
same.  The  increase  in  the  difference  is  sometimes  fa. 

101 


MEMOIRS    ON 

On  the  other  hand,  I  have  convinced  myself  many  times  that 
the  difference  of  vapor-pressure  in  two  given  tubes  is  exactly 
the  same  at  the  same  temperature,  provided  the  measurement 
is  made  after  agitation  and  in  the  manner  just  described. 

Regulation  of  the  Temperature. — We  always  work  at  the  tem- 
perature of  the  laboratory,  but  this  is  so  arranged  that  the 
temperature  can  vary  between  certain  limits  or  remain  almost 
completely  stationary.  The  laboratory  is  small,  is  on  the  north 
side,  and  the  sun  never  shines  into  it.  It  is  heated  by  a  gas- 
stove,  provided  with  a  thermo-regulator  whose  reservoir  con- 
tains 50  litres  of  air.  The  air  of  the  laboratory  is  constantly 
stirred  by  the  swinging  of  the  door  of  a  closet,  which  acts  as  a 
fan.  Thermometers  placed  to  the  right,  and  left,  above,  and 
below  the  barometric  tabes  constantly  indicate  the  same  tem- 
perature, and  this  often  remains  constant  for  hours  to  nearly 
•fy  of  a  degree. 

Measurement  of  the  Heights  of  the  Mercurial  Columns. — The 
heights  of  the  mercury  in  the  different  tubes  are  measured 
by  means  of  an  excellent  cathetometer,  of  1.50  millimetres 
range,  giving  fiftieths  of  a  millimetre.  This  instrument  rests 
firmly  on  a  column  of  masonry  covered  with  an  iron  plate.  The 
tubes  to  be  observed  are  placed  between  the  cathetometer  and 
a  well-lighted  glass  door,  so  that  the  tops  of  the  mercury  col- 
umns stand  out  clearly  in  black  against  a  light  background. 
The  end  of  the  screw  in  contact  with  the  mercury  in  the  bath 
can  be  as  easily  seen,  and  we  are  able  without  difficulty  to  de- 
termine the  vertical  distance  between  the  upper  point  of  this 
screw  and  the  level  of  the  mercury  in  each  tube.  A  normal 
barometer  placed  in  the  same  room  gives  the  atmospheric 
pressure. 

Method  of  Observation. — We  choose  a  moment  for  the  obser- 
vation when  the  temperature  and  atmospheric  pressure  are  as 
constant  as  possible.  The  tubes  containing  the  solutions  are 
shaken,  and  after  ten  minutes  the  observations  are  begun.  The 
temperature  never  being  exactly  constant,  the  levels  are  never 
absolutely  stationary.  Notwithstanding  all  this,  to  obtain  very 
accurate  results,  recourse  is  had  to  the  method  of  alternate  ob- 
servations. Two  tubes  are  observed  alternately  from  minute 
to  minute,  the  one  containing  pure  ether,  the  other  an  ethereal 
solution,  until  the  heights  in  two  successive  observations  do  not 
differ  more  than  0.2  millimetre.  If  the  heights  found,  in  three 

102 


THE    MODERN    THEORY    OF    SOLUTION 

consecutive  observations  on  each  tube,  are  in  arithmetical  pro- 
gression, the  observations  are  regarded  as  satisfactory,  and  the 
mean  of  them  is  taken.  A  single  observation,  made  at  the  end, 
gives  the  height  of  the  mercury  in  the  tube  containing  the  pure 
ether.  Another  gives  the  height  of  the  barometer. 

These  quantities  being  determined,  it  only  remains  to  know 
the  depressions  of  the  mercury  due  to  capillary  action,  and  to 
the  weight  of  the  liquid  added,  in  order  to  calculate  the  vapor- 
pressures,  /and  /',  of  pure  ether,  and  of  the  solution  under 
consideration. 

Correction  for  the  Depression  of  the  Mercury  Due  to  the 
Liquid  Placed  Above  It  and  to  Capillarity.  —  After  having 
made  all  the  observations  desired  on  a  tube,  it  is  transferred 
to  a  deep  bath  whose  upper  walls  are  of  glass.  It  is  lowered 
to  1%  its  length,  and  held  in  this  position  by  means  of  a  stand 
and  clamp.  Finally,  the  slender  drawn-out  end  is  cut.  The 
air  enters  the  tube  and  the  mercury  within  descends  below 
the  level  in  the  bath.  Enough  water  is  then  carefully  poured 
on  the  mercury  of  the  bath  to  bring  the  top  of  the  column  of 
mercury  in  the  tube  exactly  to  the  same  plane  as  the  mercury 
in  the  bath.  The  height  of  water  added  is  a  measure  of  the 
sum  of  the  pressures,  due  to  the  weight  of  liquid  placed  over 
the  mercury,  and  to  capillarity.  It  is  easy  to  estimate  it  in 
terms  of  height  of  mercury  column. 

Let  H  be  the  height  of  the  barometer,  *Ji  the  height  of  the 
mercury  in  the  tube  containing  pure  ether,  and  a  the  column 
of  mercury  equivalent  to  the  weight  of  liquid  placed  above 
it,  and  to  capillarity  ;  hf  and  a'  the  corresponding  quantities 
for  the  tube  containing  the  ethereal  solution  ;  t)  the  difference 
between  the  heights  of  mercury  in  the  two  tubes,  so  that 
c  —  li—li,  all  the  heights  being  reduced  to  zero. 

We  have,  for  the  vapor-pressure  of  pure  ether,  /  : 

/—  H—  h—  a-, 
and  for  the  vapor-pressure  of  the  ethereal  solution  examined, 


Error  Produced  by  the  Gaseous  Residue.  —  I  have  stated  that 
ether  purified  as  was  indicated  contains  a  small  quantity  of  gas 
in  solution,  from  which  it  is  very  difficult  to  free  it  completely. 
To  eliminate  as  much  as  possible  the  influence  of  this  trace 
of  gas  on  the  heights  of  the  mercurial  columns,  I  have  found 

103 


MEMOIRS    ON 

nothing  better  than  to  allow  the  vapor  formed  to  occupy  a 
large  volume.  This  is  the  reason  why  I  ^employ  very  long 
tubes,  in  which  the  vapor  formed  occupies  always  a  volume  of 
at  least  20  centimetres.  Even  under  these  conditions  the  in- 
fluence of  the  gaseous  residue  is  not  zero.  If,  for  example,  this 
residue  occupies  a  volume  of  5  cubic  millimetres  under  atmos- 
pheric pressure,  it  will  produce  a  pressure  of  0.19  millimetre 
in  a  volume  of  20  centimetres  ;  and  the  resulting  error  in  the 
measurement  of  vapor-pressure  is  nearly  T2^  of  a  millimetre, 
which  is  still  appreciable.  However,  as  all  of  the  tubes  are  pre- 
pared in  the  same  manner,  and  since  they  contain  nearly  equal 
quantities  of  the  same  ether,  the  volume  of  the  gaseous  residue 
is  everywhere  nearly  the  same.  The  influence  exerted  by  this 
residue  on  the  heights  of  the  mercurial  columns,  therefore,  dis- 
appears for  the  most  part  in  the  differences,  or  even  in  the  ratios. 

Error  Arising  from  the  Solutions  Becoming  More  Concen- 
trated, Due  to  the  Formation  of  Vapor.  —  The  weight  of  ether 
which  separates  from  the  solution  as  vapor,  to  saturate  the  rela- 
tively large  empty  space  presented  to  it,  is  often  sufficient  to 
appreciably  change  the  concentration.  But  it  is  possible  to 
calculate  the  amount  with  sufficient  accuracy,  and,  notwith- 
standing this,  to  know  the  true  concentration  of  the  solution  in 
contact  with  the  vapor. 

If  we  represent  by  n  and  ri  the  weights  of  non-volatile  sub- 
stance dissolved  in  100  grams  of  ether,  before  and  after  the 
production  of  vapor,  we  have  : 


)  76000000' 

in  which  I  is  the  length  in  centimetres  which  the  ether-vapor 
occupies  in  the  tube  ;  I',  the  length  occupied  by  the  solution  ; 
d,  the  density  of  ether-vapor  referred  to  air  (d—  2.57)  ;  d',  the 
density  of  the  solution  ;  /',  the  elastic  force  of  the  vapor  of  the 
solution  ;  t,  the  temperature  ;  a=0.00367. 

In  the  exact  calculations  n'  ought  to  be  substituted  for  n  ; 
but  if  the  temperature  is  not  high,  and  if  the  solutions  are 
dilute,  the  correction  is  reduced  to  a  mere  trifle. 
If,  for  example,  we  have  approximately  : 

n=I5,  1=30,  f  =300,  *  =  16°,  7=3,  d'=O.SO, 
it  becomes  : 

w'=1.01  +  w. 
104 


THE  MODERN  THEORY  OF  SOLUTION 

That  is,  the  formation  of  the  vapor  in  this  case  increases  the 
concentration  about  y^-.  The  correction  would  be  greater 
if  the  temperature  were  higher  and  the  solution  more  concen- 
trated. I  estimate  that,  all  corrections  made,  the  vapor-press- 
ures,/and  /',  of  the  ether  and  of  the  ethereal  solution,  can  be 
obtained  to  0.2  of  a  millimetre. 

Influence  of  Concentration  on  the  Vapor- Pressure  of  Ethereal 
Solutions. — I  could  have  wished,  for  the  sake  of  greater  sim- 
plicity, to  have  been  able  to  experiment  on  solutions  obtained 
by  mixing  absolutely  non-volatile  substances  with  the  ether. 
Unfortunately,  nearly  all  of  the  substances  soluble  in  all  pro- 
portions in  ether  have  an  appreciable  vapor -pressure  at  the 
ordinary  temperature,  and  the  best  I  could  do  was  to  select  for 
my  experiments  those  substances  whose  vapor-pressure  was  the 
smallest. 

These  are : 


BOILING-POINTS. 

o 


Oil  of  turpentine 160 

Nitrobenzene 205° 

Aniline 182° 

Methyl  salicylate 222° 

Ethyl  benzoate 213° 

At  a  given  temperature  the  vapor-pressures  of  the  last  four 
substances  are  less  than  that  of  the  oil  of  turpentine,  which  is 
known  from  the  experiments  of  Regnault,  and  which,  in  the 
neighborhood  of  15°,  is  not  one-ninetieth  of  that  of  the  ether. 
Besides,  as  I  shall  show  later,  they  are  considerably  diminished 
in  the  ethereal  solutions,  and  they  do  not  prevent  the  manifes- 
tation of  the  general  laws  which  govern  the  phenomena. 

In  the  following  tables  : 

The  first  column  gives  the  weight,  Q,  of  substance  dis- 
solved in  100  grams  of  solution.  This  is  equal  to  -  —,,  in 

which  p'  is  the  weight  of  substance  mixed  with  a  weight  p  of 
ether. 

The  second  column  gives  the  number,  n,  of  molecules  of 
substance  existing  in  100  molecules  of  the  solution.  This  is 

equal  to  — —    *^    ,  in  which  74  is  the  molecular  weight  of 
p  X  74  x pm 

ether,  and  m  that  of  the  dissolved  substance. 

105 


MEMOIRS    ON 

The  third  column  indicates  the  experimental  value  of  the 


ratio 


f 


,  between  the  vapor-pressure  of  the  solution/'  and  that 

of  pure  ether  /at  the  same  temperature.     This  ratio  has  been 
multiplied  by'lOO. 

The  fourth  column  gives  the  values  of  ^j  x  100,  calculated 
from  the  formula  : 


in  which  the  coefficient  Ovaries  with  the  nature  of  the  sub- 
stance dissolved  in  the  ether. 

Mixtures  of  Oil  of  Turpentine  and  Ether. 


Number  of  Molecules 

of  Oil  in  100  Mole- 

cules  of  Mixture. 


Temperature  of  the  experiments 16°.  2 

Vapor-pressure  of  the  oil  of  turpentine  at  the  tem- 
perature of  the  experiments 4  mm. 

Vapor-pressure  of  pure  ether  at  the  same  temperature  377  mm. 

Ratio  her  ween  the  Vapor-Press- 
ure of  the  Mixture  and  that 
of  Pure  Ether,  Multiplied 

by  100,  or  t-  x  100. 

N  Observed.  Calculated. 

(2)  (3)  (4) 

5.9 94.0.. 

12.1 88.1.. 

23.4 78.1 78.9 

50.3 35.5 67.6 68.0 

62.8 47.9 56.2 56.9 

64.5..  ..42,1..  ..42.0 


Weights  of  Oil  in 

100  Grams  of 

Mixture. 

Q 

(i) 

10.2 

20.2 

35.9.. 


94.7 

..89.1 


The  values  of  ^-x  100,  in  the  last  column,  were  calculated  by 
means  of  the  formula : 

4  X  100  =  100- 0.90  x^V. 


This  is  the  equation  of  a  straight  line  having  •—=  x  100  for  ordi- 

nates,  and  N  for  abscissae,  i.  e.,  the  number  of  molecules  of 
substance  contained  in  100  molecules  of  the  mixture. 

106 


THE    MODERN    THEORY    OF    SOLUTION 

The  agreement  between  the  results  observed  and  calculated 
is  as  satisfactory  as  could  be  desired. 

Remark.  —  The  oil  of  turpentine  after  it  has  been  distilled 
for  some  time  soils  mercury  very  badly.  To  have  it  in  proper 
condition  I  pour  a  certain  quantity  of  mercury  in  the  flask  in 
which  it  is  contained,  and  after  closing  the  flask  I  expose  it  to 
the  sun,  and  shake  from  time  to  time.  After  eight  days  I  dis- 
til over  magnesium,  in  a  condenser  with  two  bulbs,  and  I  use 
the  product  which  passes  over  at  159°  as  soon  as  it  is  obtained. 

Mixtures  of  Nitrobenzene  and  Ether. 


Temperature  of  experiment  .......................     16° 

Vapor-pressure  of  nitrobenzene  at  the  temperature  of 

experiment  ..................................       2  mm. 

Vapor-pressure  of  pure  ether  at  the  same  temperature  374  mm. 

Nitrobenzene,  prepared  from  pure  benzene,  was  purified  at 
first  by  distillation.  A  few  days  before  using  it  it  was  re- 
purified  by  repeated  crystallizations.  It  was  nearly  colorless. 


Weights  of  Nitro- 
benzene in 
100  Grams  .of 
Mixture. 

Q 
(i) 
9.6  

Number  of  Molecules      Ratio  between  the  Vapor-Press- 
of  Nitrobenzene  in          ure  of  the  Mixture  and  that 
100  Molecules  of              of  Pure  Ether,  Multiplied 

Mixture-                          by  100  or  /x  100 

y      ,     f, 

N                       Observed.               Calculated. 
(2)                             (3)                            (4) 
6.0  94.5  95.6 

26.7  

17.9.... 

85.8  

86.8 

47.2 

35.5..    . 

.  74.4 

..73.7 

65.4  

53.2  

62.0  

60.6 

80.9.. 

..75.9.. 

.  44.4.  . 

..43.8 

88.5 84.0 35.5 37.8 

f 
The  calculated  values  of  '—?  xlOO,  in  the  fourth  column  of 

this  table,  were  obtained  by  means  of  the  formula  : 
^-x  100  =  100-0. 74  xN. 

They  evidently  agree  closely  with  those  furnished  by  obser- 
vation. 

107 


MEMOIRS    ON 

Mixtures  of  Aniline  and  EtJier. 


Temperature  of  the  experiments  ...................     15°.  3 

Vapor-pressure  of  aniline  at  this  temperature  .......       3  mm. 

Vapor-pressure  of  ether  at  this  temperature  ........   364  mm. 

The  aniline  was  prepared  from  pure  nitrobenzene  and  puri- 
fied by  distillation.     It  was  colorless. 


Ratio  between  the  Vapor-Press- 
Weights  of  Ani-      Number  of  Molecules        ure  of  the  Mixture  and  that 
line  in  100  Grams         of  Aniline  in  100  <>f  Pure  Ether,  Multiplied 

of  Mixture.  Molecules  of  Mixture.  by  100,  or  f-  x  100. 


Q 

(i) 
4.8.. 

N 
(2) 
3.85.. 

Observed. 
(3) 
96.0  

Calculate 
(4) 
96.6 

9.5.. 
18.1.. 

7.7  .. 
14.8   .. 

91.9  
84.5 

93.1 

86  7 

24.5.. 
55.3.. 
73.4.. 

20.5   .. 
49.6   .. 

..68.7  . 

80.3  
57.6  
40.4.. 

81.6 
55.4 
..38.2 

f 

The  calculated  values  of  ^  x  100,  in  the  fourth  column,  were 

obtained  by  means  of  the  formula : 

^-x  100=100-0.90  xN. 
They  agree  fairly  well  with  the  results  of  observation. 

Mixtures  of  Methyl  Salicylate  and  Ether. 


Temperature  of  the  experiments 14°.  1 

Vapor-pressure  of  methyl  salicylate  at  this  tempera- 
ture         2  mm. 

Vapor-pressure  of  ether  at  the  same  temperature. . . .  346  mm. 

108 


THE    MODERN    THEORY    OF    SOLUTION 


Weights  of  Sali- 

Number  of  Molecules 

nauo  oeiwee 

Tivfni»*i    o»ir1    +V»oi- 

cylate  in 
100  Grams  of 

of  Salicylate  in  100 
Molecules  of 

of  Pure  Ether,  Multiplied 

Mixture. 

Mixture. 

by  100, 

or-L_x  100. 

Q 

N 

Observed. 

Calculated. 

(1) 

(2) 

(3) 

(4) 

2  256 

1.1        . 

99.6.  .  . 

99.1 

4  20 

.  .   2.1.  . 

..    .  99.3... 

98.3 

9  4 

..   4.8  

..  .  96.0... 

96.1 

17.3 

.      ..   9.2  

91.4... 

92.5 

26.8     .  . 

15.1  

.  .  .  .  87.0.  .  . 

87.6 

38  6 

.23.2  

81.1... 

81.0 

66.4     .  . 

49.0  

....  60.0... 

59.8 

87.3     .  . 

77.0  

....  36.1... 

36.9 

91.4 

..85.0  

....  29.2... 

30.3 

The 


f 

values  of  ^  X 100, 


fourth  column,  were 


obtained  by  means  of  the  formula: 

•-Cx  100 =100— 0.82 

The  agreement  between  the  calculated  and  the  observed  re- 
sults is  quite  remarkable. 

Mixtures  of  Ethyl  Benzoate  and  Ether. 
C9  ffio  02  =  150. 

Temperature  of  the  experiments 11°.  7 

Vapor-pressure  of  ethyl  benzoate  at  this  temperature.       3  mm. 
Vapor-pressure  of  pure  ether  at  the  same  temperature  313  mm. 

The  ethyl  benzoate  was  purified  by  the  ordinary  method.     It 
nearly  all  distilled  over  at  213°. 

Weights  of  Ethyl     Number  of  Molecules 


ienzoaie  in 
0  Grams   of 

100  Molecules  of              of  Pure  Ether,Multiplied 

Mixture. 

Mixture. 

by  100,  or 

'—x  100. 

Q 

N 

Observed. 

Calculated. 

(1) 

(2) 

(3; 

(4) 

9.4.... 

4.9.. 

94.9  

95.6 

17.7.... 

9.6.. 

90.9  

91.4 

43.0.... 

27.1.. 

75.2  

75.6 

69.6.... 

53.0.. 

52.9  

52.3 

86.2.... 

75.5.. 

30.0  

32.1 

97.1.... 

94.4.. 

12.4  

15.0 

109 


MEMOIRS    ON 

f 

The  calculated  values  of  ~  x  100,  in  the  last  column,  were 

obtained  with  the  aid  of  the  formula  : 

fj  x  100  =  100-0.90  x  N-, 

and  here,  also,  they  agree  satisfactorily  with  the  values  found 
by  experiment. 

General  Results.—  We  see  that  for  the  different  mixtures 
studied  the  results  obtained  agree  pretty  well,  as  a  whole, 
with  the  results  calculated  by  means  of  the  formula  : 


(1)  x  100=100- 

in  which  N  is  the  number  of  molecules  of  non-volatile  sub- 
stance existing  in  100  molecules  of  the  mixture,  and  K  a  co- 
efficient which  depends  only  upon  the  nature  of  the  substance 
mixed  with  the  ether. 

It  should  be  observed  that  the  coefficient  ./T  generally  varies 
but  little  with  the  nature  of  the  dissolved  substance,  and  it  is 
usually  very  nearly  unity.  Its  values  for  the  following  sub- 
stances are  : 

Oil  of  turpentine  in  ether  ............   K  —  0.90 

Aniline  in  ether  .....................   K  '  —  0.90 

Ethyl  benzoate  in  ether  ..............   K=  0.90 

Methyl  salicylate  in  ether  ............   K  '=  0.82 

Nitrobenzene  in  ether  ................   K  =  0.70 

I  made  similar  experiments  on  mixtures  of  carbon  bisulphide 
with  different  substances  as  slightly  volatile  as  the  above. 
These  experiments,  an  account  of  which  will  be  given  later, 

f 

prove  that  the  ratio  ~  varies,  in  this  case,  with  the  concentra- 

tion, according  to  the  same  laws  as  in  the  ethereal  solutions  ; 
and  that  in  formula  (1),  which  sums  them  up,  the  coefficient 
K  is  also  a  little  less  than  unity.  This  formula  ought,  there- 
fore, until  the  contrary  is  proven,  to  be  considered  as  applica- 
ble to  the  calculation  of  the  vapor  -pressures  of  all  volatile 
liquids  employed  as  solvents. 

We  will  now  avail  ourselves  of  it  to  determine  to  what  extent 
the  preceding  results  are  modified  by  the  vapor-pressure  of  the 
substances  mixed  with  the  ether. 

Influence  of  the  Vapor-  Pressure  of  the  Substances  Mixed  witli 

110 


THE    MODERN    THEORY   OF 

the  Ether.  —  Let  ^  be  the  vapor-pressure  which  the  dissolved 
substance  possessed  when  pure;  ^',  the  vapor  -pressure  of  the 
same  substance  when  mixed  with  the  ether  ;  N't  the  number 
of  molecules  of  ether  in  100  molecules  of  the  mixture. 

The  vapor-pressure  /'  of  an  ethereal  solution,  being  the  sum 
of  the  partial  pressures  of  the  ether  and  of  the  dissolved  sub- 
stance, the  partial  pressure  of  the  ether  vapor  in  the  mixture 
is  /*'_  0.  But  from  formula  (1),  which  finds  here  a  legitimate 
application  : 


From  this  we  have  : 


or  in  dividing  by/,  the  tension  of  pure  ether: 
(3) 


f       -f      f          100 

fl  _  ,' 

the  exact  value  of  the  ratio  J  f  ,  which  exists  between  the 
vapor  -  pressures  of  the  ether  in  the  mixture,  and  when  pure, 
is  obtained,  therefore,  by  cutting  off  the  term  y(l  — 

f 

from  the  crude  ratio  y 

But  in  all  of  the  preceding  experiments  the  ratio  ~  between 

the  tension  of  the  dissolved  substance  and  that  of  the  ether, 
both  considered  as  pure,  is  less  than  ^.  The  correction  term 

~  1  1—  -)  is,  therefore,  always  less  than  ^,  and  it  becomes 
/  \  100  / 

less  than  jfa  for  the  values  of  N'  which  are  greater  than  50. 
It  is,  consequently,  always  negligible  in  comparison  with  the 
experimental  errors.  The  influence  of  the  vapor  -  pressure  of 
the  substances  mixed  with  the  ether  is,  therefore,  too  slight  to 
be  introduced  as  a  correction  into  the  results  obtained. 

Causes  of  Error  in  Concentrated  Solutions.  —  There  are  some 
differences  between  the  results  observed  and  those  calculated 
by  formula  (1),  and  these  appear  especially  with  very  concen- 
trated or  very  dilute  solutions. 

As  far  as  the  very  concentrated  solutions  are  concerned,  in 

111 


MEMOIRS    ON 

which  Nis  greater  than  70 — i.  e.9  in  which  there  are  more  than 
70  molecules  of  non-volatile  substance  to  100  molecules  of 
mixture — the  differences  are  perhaps  due  only  to  errors  of  ex- 
periment. The  determinations  then  become  very  difficult  in- 
deed. In  such  mixtures  the  proportion  of  ether  is  very  slight, 
and  however  little  ether  is  lost  by  evaporation  during  the  trans- 
fer, a  loss  which  is  inevitable,  the  solutions  become  more  con- 
centrated and  their  vapor-pressures  too  small.  Moreover,  it  may 
happen  that  the  liquid  layers  in  contact  with  the  vapor  in  the 
barometric  tubes,  become  more  concentrated  than  the  deeper 
layers,  notwithstanding  the  shaking ;  and  in  this  case,  again, 
their  vapor-pressure  would  be  too  slight. 

Laws  delating  to  Dilute  Solutions. — For  solutions  which  are 
dilute  and  in  which  N  is  less  than  15,  the  differences  disappear 
for  the  most  part  if  in  formula  (1)  K  is  made  equal  to  1. 
Indeed,  in  this  case  the  results  of  experiment  agree  nearly  al- 
ways to  -g-J-g-  with  those  given  by  the  formula  : 

(4)  ^-'xioo=ioo-jv. 

To  show  this  important  fact,  I  give  in  the  following  table  the 
results  calculated  by  means  of  this  formula  (4),  together  with 
the  results  observed  with  different  dilute  solutions,  for  which 
15 : 


SUBSTANCE  DIS-       MOLECULAK  CON-                      J_ 

100. 

SOLVED   IN                  CENTRATION.                             / 

DIFFER- 

ETHER. 

A~. 

CALCULATED. 

OBSERVED. 

ENCE. 

Oil  of  turpentine. 

j    5.9 
(12.1 

94.1 

87.9 

94.0 

88.1 

•sir 

•sir 

Nitrobenzene  

6.0 

94.0 

94.5 

Th 

Aniline        

j    3.85 

(    7.7 

96.2 
92.3 

96.0 
92.3 

T*F 

0 

r  1.1 

98.9 

99.6 

T!T 

Methyl  salicylate. 

97.9 
95.2 

99.3 
96.0 

iWr 

I   9.2 

90.8 

91.4 

6 

Ethyl  benzoate.  .. 

{  t:l 

95.1 
90.4 

94.9 
90.9 

¥ 

~§-Q-$ 

We  see  that  the  difference  between  the  results  observed  and 
calculated  seldom  exceeds  -^  of  their  value.     There  is  an 

112 


THE    MODERN    THEORY    OF    SOLUTION 

exception  only  for  extremely  dilute  solutions  —  i.  e.,  those  in 
which  N  is  less  than  2,  which  seem  to  follow  a  more  compli- 
cated law.  But  it  appears  to  me  to  be  hardly  possible  to  make 
any  assertion  regarding  them  ;  determinations  of  this  kind  be- 
coming more  and  more  difficult  and  uncertain  as  the  dilution 
increases. 

Formula  (4)  is,  therefore,  in  accord  with  experiment,  as  far 
as  could  be  desired,  as  long  as  the  values  of  N  are  between 
2  and  15. 

Comparison  with  the  Law  of  Wtillner.  —  Different  physicists, 
and  particularly  Von  Babo  and  Wiillner,  have  shown  that  for 
certain  solutions  of  salt  in  water  the  relative  diminution  of 

f—f 
pressure  •          is  practically  proportional  to  the  weight  of  salt 

dissolved  in  a  constant  weight  of  water.  This  can  be  expressed 
by  the  formula  : 

(5)  £xlOO  =  100-JTJrx-^, 

K  being  a  constant  coefficient  for  each  substance. 

This  expression  differs  considerably  from  formula  (4)  ;  but 
it  should  be  observed  that  the  latter  applies  especially  to 
ethereal  solutions,  for  which  N>3.  Often  when  _Y<3,  for- 
mula (4)  applied  to  aqueous  solutions  gives  results  which  are  too 
large,  and  then  formula  (5)  advantageously  replaces  it.  Besides 
this  special  case,  formula  (5)  gives,  even  for  aqueous  solutions, 
information  which  is  more  and  more  erroneous  as  N  becomes 

f 

greater.     In  addition,  it  leads  to  negative  values  for  J—  when 

wx.    10° 

TV  >^  —  -,  which  is  absurd. 


These  variations  very  probably  result  from  the  fact  that  the 
condition  of  the  substance  in  the  solutions  changes  with  the 
concentration  ;  and  we  ought  to  be  astonished  that,  notwith- 
standing all  this,  we  can  express  the  vapor-pressure  f  of  the 
ethereal  solutions  by  means  of  two  relations  which  are  also  sim- 
ple ;  the  one,  (1),  giving  the  values  of  /'  at  least  to  about  ^, 
for  all  the  values  of  A^from  0  to  70  ;  the  other,  (4),  giving  them 
to  about  y^j-  for  all  the  values  of  N  between  3  and  15. 

Particular  Expression  of  the  Law  relating  to  Dilute  Solu- 
tions. —  Formula  (4),  relating  to  dilute  solutions,  acquires  an 
interesting  form  if  were  place  ^Vby  100  —  JV',  the  quantity  N 
H  113 


MEMOIRS    ON 

being  the  number  of  molecules  of  ether  contained  in  100  mole- 
cules of  the  mixture.  This  formula  then  becomes  transformed 
into  the  following  : 

(6)  £xlOO  =  JV', 

which  is  to  say  that,  in  ethereal  solutions  of  medium  concentra- 
tions, the  partial  pressure  of  the  ether  vapor  is  proportional  to  the 
number  N',  of  molecules  of  ether  existing  in  100  molecules  of  the 
mixture,  and  is  independent  of  the  nature  of  the  dissolved  sub- 
stance. I  shall  return  again  to  the  last  point. 

Influence  of  Temperature  on  the  Vapor  -  Pressure  of  Ethereal 
Solutions. — To  study  the  influence  of  temperature  I  placed 
four  barometric  tubes,  containing  the  dilute  solutions  obtained 
by  mixing  different  high-boiling  substances  with  the  ether,  in 
the  same  mercury  bath  for  several  months.  I  then  measured 
the  vapor-pressure  very  carefully  whenever  the  circumstances 
were  favorable.  Although  in  this  interval  the  temperature 
varied  from  0°  to  22°,  I  always  found  approximately  the  same 

f 

value  for  the  ratio  — 

Some  of  the  results  obtained  are  collected  in  the  following 
tables,  t  is  the  temperature,/  the  vapor-pressure  of  pure  ether, 
and/'  the  vapor-pressure  of  the  solution. 


Mixture  of  16.482  Grams  of  Oil  of  Turpentine  and  100  Grams  of  Ether. 

t  f  f  ^XlOO 

l°.l 199.0 188.1 '.91.5 

3°.6 224.0 204.7 91.4 

18°.2 408.5 368.7 91.0 

21°.8 ,.472.3 430.7 91.2 

Mixture  of  10.442  Grams  of  Aniline  with  100  Grams  of  Ether, 
t  f  f  ^xlOO 

l°.l 199.5 183.3 91.9 

3°.6 223.2 204.5 91.6 

9°.9 289.1 264.0 91.3 

21°.8 472,9 432.7 91.5 

114 


THE    MODERN    THEORY    OF    SOLUTION 

Mixture  of  27.601  Grams  of  Hexachlorethane  with  100  Grams  of  Ether. 
t  f  f  £xlOO 

1°.0 197.0 181.3 92,0 

3°.7 224.2 205.4 91.6 

18°.8 418.6 280.9 91.0 

21°.0 457.3 417.8 91.4 

Mixture  of  12.744  Grams  of  Benzoic  Acid  and  100  Grams  of  Ether. 

t  f  f  —  xlOO 

j  j  f 

3°.8 224.1 209.5 93.5 

18°.4 412.6 382.0 92.6 

21°.7 470.2 431.2 91.7 

These  tables  show  that  for  the  solutions  of  oil  of  turpentine, 
of  aniline,  of  hexachlorethane,  the  value  of  the  ratio  ^  does 

not  vary  more  than  0.5  in  100,  when  the  temperature  changes 
from  0°  to  21°.  This  variation  is  very  slight  and  scarcely  ex- 
ceeds that  often  observed  in  two  consecutive  experiments,  made 
on  the  same  solution  under  the  same  conditions. 

The  variation  for  the  solution  of  benzoic  acid  is  a  little 
greater,  but  this,  perhaps,  depends  upon  a  chemical  reaction 
which  takes  place  in  time  between  the  substances  mixed  with 
one  another. 

It  is  worth  observing  that  the  influences  of  the  vapor-press- 
ure of  the  substances  mixed  with  the  ether  is,  even  here,  en- 

f 

tirely  incapable  of  appreciably  modifying  the  ratio,  ~.     The 

f 

quantity  by  which  '-—  is  increased  is,  indeed,  as  indicated  by 

formula  (3) : 


*  L     KN'\ 

(     IST/' 


But  for  the  oil  of  turpentine,  which  is  the  most  volatile  of 
all,  we  have  : 


115 


MEMOIRS    ON 

Moreover,  in  all  of  these  solutions  we  have  JV>  90  and  K  is 
approximately  1.  The  result  is  that  the  quantity,  (q),  to  be 

f 

subtracted  from  —  -  is  : 

s 

<  0.00108  at  0° 

<  0.00106  at  20°  ; 

that  is,  it  is  completely  negligible  in  comparison  with  this  ratio, 
which  is  here  almost  unity.  It  can  all  the  more  be  rejected  for 
the  other  solutions. 

Finally,  the   preceding   experiments    show   that    the    ratio 

f 

'—  is  independent  of  the  temperature  between  0°  and  21°. 

Influence  of  the  Nature  of  the  Dissolved  Substance  on  the 
Vapor-Pressure  of  Ethereal  Solutions. — The  vapor-pressure,/', 
of  a  solution  of  a  non-volatile  substance  in  ether,  the  vapor- 
pressure  of  the  pure  ether,/,  at  the  same  temperature,  and  the 
number,  N,  of  molecules  of  non-volatile  substance  existing  in 
100  molecules  of  the  mixture,  are,  as  we  have  already  seen, 
united  by  the  equation  : 


(1)  =yx  100=100-. 

We  can  give  to  this  expression  the  following  form : 

(7)  ££  =  *?. 

/         100 

The  ratio  ,  being  what  is  called  the  relative  diminution  of 

vapor-pressure  of  the  solution  in  question,  formula  (7)  can  be 
translated  into  ordinary  language  thus  : 

For  all  of  the  ethereal  solutions  of  the  same  nature,  the  relative 
diminution  of  vapor-pressure  is  proportional  to  the  number  of 
molecules  of  non-volatile  substance  dissolved  in  100  molecules  of 
the  mixture. 

We  have  seen,  also,  that  where  the  solutions  are  dilute,  and 
where  N  is  less  than  15,  the  coefficient  K  is  unity,  and  we 
have : 


That  is,  if  we  divide  the  relative  diminution  of  pressure  :—^~ 

of  a  dilute  ethereal  solution  by  the  number,  N,  of  molecules  of 

116 


THE    MODERN    THEORY    OF    SOLUTION 

non-volatile  substance  existing  in  100  molecules  of  the  mixture,  we 
obtain  as  a  quotient  0.01,  whatever  the  nature  of  this  substance. 
With  a  view  to  ascertain  whether  this  remarkable  law  is  gen- 
eral, I  dissolved  in  ether  compounds  taken  from  the  different 
chemical  groups,  and  chosen  from  those  whose  boiling-points 
are  the  highest ;  the  compounds  having  molecular  weights 
which  are  very  widely  different  from  one  another;  and  I  meas- 
ured the  vapor-pressures  of  the  solutions  obtained.  In  every 

f—f 
case  I  found,  as  we  will  see,  that  the  ratio  '     '     is  very  nearly 

0.01,  as  is  required  by  formula  (8). 

The  substances  which  I  employed  are,  for  the  most  part,  well 
known  to  chemists,  and  it  would  be  uninteresting  to  state  here 
how  they  were  prepared  and  purified.  I  shall,  therefore,  limit 
myself  to  giving  some  particular  information  in  reference  to  the 
rarest  of  them,  which  are  methyl  nitrocuminate  and  cyanic  acid. 

The  methyl  nitrocuminate,  C22H26  N2  04=382,  was  prepared 
from  a  beautiful  sample  of  very  pure  nitrocuminic  acid,  ob- 
tained by  M.  Alexeyeff.  This  acid  was  introduced  into  pure 
methyl  alcohol,  and  a  current  of  hydrochloric -acid  gas  was 
passed  through  the  alcohol.  When  the  reaction  was  over,  the 
liquid  was  evaporated  to  dryness.  Finally,  the  product  ob- 
tained was  purified  by  several  crystallizations  from  methyl 
alcohol.  This  is  a  beautifully  crystallized  substance,  of  an 
orange-red  color,  giving  with  ether  a  nearly  red  solution.  Its 
molecular  weight,  established  with  certainty  by  the  cryoscopic 
method,  is  very  high,  and  this  is  the  reason  which  led  me  to 
use  it. 

Cyanic  acid,  HOCN=4=3,  was  prepared  in  the  open  air  when 
it  was  very  cold,  by  distilling  dry  and  pure  cyanuric  acid.  After 
nitration,  it  was  introduced  at  —3°  into  a  tared  vessel  with 
thin  walls  which  had  been  previously  exhausted.  This  vessel 
was  weighed,  then  broken  in  a  known  weight  of  very  cold 
ether.  The  solution  obtained  was  introduced  into  a  baro- 
metric tube,  and  the  air  and  gases  dissolved  in  it  were  care- 
fully extracted,  always  in  the  cold.  The  vapor-pressure  of  the 
solution  was  measured  first  at  —1°.  To  my  great  surprise  the 
ethereal  solution  contained  in  the  barometric  tube  was  not 
changed,  even  after  two  days,  at  the  temperature  of +6°,  and 
I  was  able  'to  make  several  determinations  at  this  temperature 
which  confirmed  the  results  of  the  first. 

117 


MEMOIRS    ON 

Some  substances,  particularly  those  containing  chlorine,  not- 
withstanding the  most  careful  purifications,  still  have  the  very 
inconvenient  property  of  soiling  mercury.  To  deprive  them 
of  this  property  it  is  only  necessary  to  expose  them  to  the  sun 
in  contact  with  mercury,  in  completely  filled  bottles,  shaking 
them  from  time  to  time.  Exposure  for  a  few  days  generally 
suffices,  if  the  light  is  intense. 

The  following  table  summarizes  the  results  which  were  ob- 
tained at  about  15°,  with  solutions  containing  from  4  to  12 
molecules  of  non-volatile  substance  to  100  molecules  of  mixt- 
ure. In  this  table  : 

Column  (1)  contains  the  names  of  the  slightly  volatile  sub- 
stances dissolved  in  the  ether ; 

Column  (2)  gives  the  chemical  formula  and  the  molecular 
weight,  M,  of  these  substances  ; 

Column  (3)  shows  the  number  of  molecules  of  substance  dis- 
solved in  100  molecules  of  mixture  ; 

f—f 
Column  (4)  contains  the  values  of  the  ratio,  ,  i.  e.,  the 

relative  lowerings  of  vapor-pressure ; 

f—f 

Column  (5)  gives  the  values  of  the  quotient,      ^  • 


(1)  (2) 

Hexachlorethane CZC16  =  237 

Oil  of  turpentine. Clo  H16  =  136 

Nitrobenzene <76  U5  N02  =  123 

Methyl  salicylate <?8  ffs  03  =  152 

Methyl  nitrocuminate. . .    C.^  H^  JV2  04  =  382 

Ethyl  benzoate C9H10  Oa  =  150 

Cyanic  acid CNOH=4S 

Benzoic  acid C7  H6  02  =  122 

Trichloracetic  acid <72  Cla  02 II—  163.5 

Benzoic  aldehyde C,  H6  0  =  106 

Caprylic  alcohol Cs  H19  0  =  130 

Aniline C6H,N=m 

Mercury  ethyl C^Htoffg=25S 

Antimony  chloride Sb  C13  =  228.5 


A' 

£-~ 

—~f- 

(3) 

(4) 

(S) 

7.93 

0.00288 

0.0100 

8.95 

0.0885 

0.0099 

600 

0.1424 

0.0084 

9.20 

0.086 

00094 

2.91 

0.026 

0.0089 

9.60 

0.091 

0.0095 

4.52 

0.041 

0.0091 

7.175 

0.070 

0.0097 

11.41 

0.120 

0.0105 

12.98 

0.132 

0.0102 

6.27 

0.070 

0.0110 

7.66 

0.081 

0.0106 

9.75 

0.089 

0.0091 

4.27 

0.037 

0.0087 

Mean 

0.0098 

I  have  given,  intentionally,  the  results  relating  to  solutions 

118 


THE    MODERN    THEORY    OF    SOLUTION 

which  were  of  very  different  concentrations,  and  in  which  N 
varied  from  3  to  13.     Notwithstanding  this,  the  values  of     .  ' 

deviate  relatively  little  from  the  mean  0.0098,  and  this  mean  is 
itself  remarkably  near  to  the  theoretical  value,  which  is  0.0100. 

This  suffices  to  show  that  formula  (8)  expresses,  with  as  much 
accuracy  as  we  could  expect,  the  law  of  vapor-pressures  of  ethe- 
real solutions,  within  the  limits  of  concentration  indicated. 

Another  Expression  of  the  Laiv.  —  This  law  can  be  presented 
in  still  another  way  : 

If  R  is  the  number  of  molecules  of  non-volatile  substance 
dissolved  in  100  molecules  of  ether,  we  have  : 

100  x  R 
~ 


Substituting  this  value  for  JVin  (8),  it  becomes  : 
/—  /'  1 

TTT  "loo+TT 

As  R  decreases  —  i.  e.,  as  the  solution  becomes  more  dilute  — 

f—f 
the  ratio'   ..;   tends,  therefore,  towards  0.01,  just  as  the  ratio 

f—f 

'   .  '    ;  and  experiment  shows  that  it  generally  reaches  this  value 

as  soon  as  R=.\.     We  can  therefore  say: 

If  we  dissolve  1  molecule  of  any  non-volatile  substance  in  100 
molecules  of  ether,  the  vapor-pressure  of  the  ether  is  diminished 
by  a  fraction  of  its  value  which  is  nearly  constant,  and  approx- 
imately equal  to  0.01. 

It  is,  indeed,  in  this  form  that  I  at  first  stated  the  law  relat- 
ing to  the  vapor  -pressures  of  the  ethereal  solutions  (Compt. 
rend.,  December  6,  1886).  But  the  statement  corresponding 
to  formula  (8)  is  more  exact  and  more  general. 

Determination  of  Molecular  Weights.  —  It  is  possible  to  turn 
to  account  the  preceding  results  in  order  to  determine  the 
molecular  weights  of  only  slightly  volatile  substances  which 
are  soluble  in  ether. 

Let  P  be  the  weight  of  a  relatively  non-  volatile  substance 
dissolved  in  100  grams  of  ether  ;  74,  the  molecular  weight  of 
ether;  M,  the  molecular  weight  of  the  dissolved  substance;  N, 
the  number  of  molecules  of  non-volatile  substance  dissolved  in 
100  molecules  of  mixture. 

119 


MEMOIRS    ON 

We  have : 

N  74xP 


100      lOOx  Jf+74xP 

N 
Substituting  this  value  of  -^  in  (4),  it  becomes,  when  finally 

1UU 

transformed  : 


(10)  Jf= 

— 
for  the  molecular  weight,  M,  of  the  substance  dissolved  in  the 

ether. 

It  is  clear  that  the  value  of  M,  thus  calculated,  can  be  only 
approximate.  But  if  the  boiling  -  point  of  the  dissolved  sub- 
stance is  higher  than  140°,  this  value  is  always  sufficiently 
close  to  the  true  value  to  determine  the  choice  between  sev- 
eral possible  molecular  weights.  It  is  not  even  necessary  for 
this  purpose  that  the  solutions  be  very  dilute  ;  and  we  always 
obtain  results  which  are  sufficiently  exact,  observing  only  this 
condition,  that  the  weight,  P,  of  substance  dissolved  in  100 
grams  of  ether  is  not  greater  than  20  grams. 

Below  are  some  examples,  taken  at  random,  which  give  an  idea 
of  the  degree  of  approximation  usually  reached  by  this  process  : 

Oil  of  Turpentine. 
In  one  experiment  I  had  : 
Weight,  P,  of  oil  (100  grams  of  ether)  ...........     11.346  gr. 

Vapor-pressure  of  the  solution/'  ................   360.1   mm. 

Difference  between  the  vapor-pressure  of  ether  and 

that  of  the  solution/—/'  ...................     22.9   mm. 

These  values  introduced  into  formula  (10)  gave  : 

M=132. 

But  we  know  that  the  true  value  of  M  for  oil  of  turpentine  is 
136.     The  difference  is  only  1  in  34. 

Aniline. 

Weight,  P,  of  aniline  in  100  grams  of  ether  ......     10.442  gr. 

Vapor-pressure  of  the  solution  /'  ................   210.8   mm. 

Difference  between  the  vapor-pressure  of  ether  and 

that  of  the  solution  /—  /'  ...................     18.8  mm. 

from  which:  Jf=87, 

a  value  which  is  nearer  to  the  true  molecular  weight,  93,  than 

to  any  other  possible  value. 

120 


THE  MODERN  THEORY  OF  SOLUTION 

Ethyl  Benzoate. 
Results  of  experiment : 

P=  21.517  gr. 
/'=284.5  mm. 
/-/'=  28.6  mm. 
Result:  .   Jf=159.2, 

which  differs  from  the  true  molecular  weight,  150,  by  1  part 
in  15. 

Benzole  Acid. 

Results  of  experiment : 

p=  12.744gr. 
/'-382.0  mm. 
/-/'=  28.9  mm. 
from  which :  Jf=124.6, 

instead  of  122,  which  is  the  exact  molecular  weight. 

We  see  from  these  examples,  that  by  observing  the  vapor- 
pressure  of  an  ethereal  solution,  we  can  easily  ascertain  which 
of  several  possible  values  is  the  true  molecular  weight  of  a  sub- 
stance. 

I  do  not  believe,  however,  that  it  is  often  advantageous  to 
have  recourse  to  this  new  means  of  determining  molecular 
weights.  It  is,  indeed,  rather  delicate  to  carry  out,  and  is  suc- 
cessfully applicable  only  to  substances  which  boil  above  140°. 
Besides,  the  cryoscopic*  method,  based  on  the  observation  of  the 
freezing-point  of  solutions  in  water,  in  acetic  acid,  or  in  ben- 
zene, furnishes  a  means  of  arriving  at  the  same  result,  which  is 
incomparably.easier,  more  exact,  and  more  general.  It  is,  there- 
fore, only  in  the  exceptional  case  that  the  substance  under  con- 
sideration is  insoluble  in  acetic  acid  and  soluble  in  ether  that 
it  is,  perhaps,  expedient  to  make  use  of  the  method  based  on 
the  measurement  of  the  vapor-pressure  of  ethereal  solutions. 

I  shall  show  in  a  subsequent  paper  that  the  same  laws  apply 
to  the  vapor -pressure  of  all  volatile  liquids,  whatsoever,  em- 
ployed as  solvents,  also  to  the  volatility  of  the  dissolved  sub- 
stance itself,  and  I  shall  deduce  from  them  the  particular  laws 
relating  to  the  vapor  -  pressures  of  mixtures  of  two  volatile 
liquids. 

*  Compt.  rend.,  Nov.  23,  1885;  Ann.  Chim.  Phys.,  [6],  8  (July, 

121 


THE    GENERAL    LAW   OF    THE   VAPOR- 
PRESSURE   OF   SOLVENTS 

BY 

F.  M.  RAOULT 

Professor  of  Chemistry  in  Grenoble 
(Comptes  rendus,  1O4,  1430,  1887) 


THE  GENERAL  LAW  OF  THE  VAPOR- 
PRESSURE  OP  SOLVENTS* 

BY 

F.  M.  KAOULT 

THE  molecular  lowering,  K,  of  the  vapor-pressnre  of  a  solu- 
tion —  i.  e.,  the  relative  diminution  of  pressure  produced  by  one 
molecule  of  non-volatile  substance  in  100  grams  of  a  volatile 
liquid  —  can  be  calculated  from  the  following  formula  : 


in.  which  /  is  the  vapor-pressure  of  the  pure  solvent,  f  that  of 
the  solution,  M  the  molecular  weight  of  the  dissolved  sub- 
stance, P  the  weight  of  this  substance  dissolved  in  100  grams 
of  the  solvent  ;  on  the  assumption  that  the  relative  diminution 

/—  f 
of  pressure,       '    ,  is  proportional  to  the  concentration.     Since 

this  proportionality  is  seldom  rigid,  even  when  the  solutions  are 
very  dilute,  I  have  endeavored  in  these  comparative  studies  to 
always  work  on  solutions  having  nearly  the  same  molecular  con- 
centration, and  containing  from  4  to  5  molecules  of  non-volatile 
substance  to  100  molecules  of  volatile  solvent.  A  greater  dilu- 
tion would  not  permit  of  measurements  which  are  sufficiently 
exact.  All  of  the  experiments  were  carried  out  by  the  baro- 
metric method,  and  conducted  like  those  which  I  made  on 
ethereal  solutions.  (Compt.  rend.,  16  Dec.,  1886.)  The  tubes 
were  dipped  into  a  water  -bath  with  parallel  glass  sides,  con- 
stantly stirred,  and  heated  at  will. 

In  each  case  the  temperature  was  so  chosen  that  the  vapor- 
pressure  of  the  pure  solvent  was  about  400  millimetres  of  mer- 
cury. The  measurements  were  completed  in  from  fifteen  to 

*  Compt.  rend.,  1O4,  1430  (1887) 
125 


MEMOIRS    ON 

forty-five  minutes  after  stirring  the  contents  of  each  tube,  the 
temperature  being  constant. 

I  employed  as  solvents  twelve  volatile  liquids — water, 
phosphorus  trichloride,  carbon  bisulphide,  tetrachlormethane, 
chloroform,  amylene,  benzene,  methyl  iodide,  ethyl  bromide, 
ether,  acetone,  and  methyl  alcohol. 

I  dissolved  in  water  the  following  organic  substances  :  Cane- 
sugar,  glucose,  tartaric  acid,  citric  acid,  and  urea.  All  of  these 
substances  produced  nearly  the  same  molecular  lowering  of 
the  vapor  -  pressure :  JT=0.185.  I  have  omitted  here  the 
mineral  compounds ;  the  action  of  these  substances  has,  in- 
deed, been  determined  by  experiments  which  are  sufficiently 
numerous  and  conclusive,  carried  out  by  Wiillner  (Pogg.  Ann., 
103  to  110,  1858-1860),  by  myself  (Compt.  rend.,  87,  1878), 
and,  very  recently,  by  M.  Tammann  ( Wied.  Ann.,  24,  1885). 

In  solvents  other  than  water  I  have  dissolved  substances  as 
slightly  volatile  as  possible,  and  have  generally  chosen  them 
from  the  following :  oil  of  turpentine,  naphthalene,  anthracene, 
hexachlorethane  (C2C16),  methyl  salicylate,  ethyl  benzoate, 
antimony  trichloride,  mercury  ethyl,  benzoic,  valeric,  trichlor- 
acetic  acids,  thymole,  nitrobenzene,  and  aniline.  The  error 
due  to  the  vapor  -  pressure  of  these  compounds  can  often  be 
neglected.  The  vapor-pressure  of  dissolved  substances  is,  in- 
deed, considerably  reduced  by  mixing  them  with  a  large  excess 
of  solvent ;  and  if,  at  the  temperature  of  the  experiment,  the 
vapor-pressure  does  not  exceed  5  to  6  millimetres,  it  does  not 
exert  any  perceptible  influence  on  the  results. 

The  molecular  lowerings  of  vapor  -  pressure,  produced  by 
these  different  substances  in  a  given  solvent,  are  grouped 
about  two  values,  of  which  the  one,  which  I  call  normal,  is 
twice  the  other.  This  normal  lowering  is  always  produced  by 
the  simple  hydrocarbons,  and  chlorides,  and  by  the  ethers  ; 
the  abnormal  lowering  almost  always  by  the  acids.  There  are, 
however,  solvents  in  which  all  of  the  dissolved  substances  pro- 
duce the  same  molecular  lowering  of  vapor-pressure;  such,  for 
example,  as  ether  (loc.  cit.)  and  acetone. 

Of  the  volatile  solvents  examined,  I  have  studied  carefully 
the  lowering  of  the  freezing-point  of  two — water  and  benzene 
(Compt.  rend.,  95  to  1O1,  and  Ann.  Chim.  Phys.,  [5],  28, 
[6],  2  and  8).  A  comparison  of  the  results  obtained  shows 
that  for  all  of  the  solutions  in  a  given  solvent  there  is  nearly  a 

126 


THE  MODERN  THEORY  OF  SOLUTION 

constant  ratio  between  the  molecular  lowering  of  the  freezing- 
point  and  the  molecular  lowering  of  the  vapor-tension.  This 
ratio  in  water  is  100,  in  benzene  60  within  -fa. 

If  we  divide  the  molecular  lowering  of  vapor  -  pressure,  K, 
produced  in  a  given  volatile  liquid,  by  the  molecular  weight  of 

J£ 

this  liquid,  M',  the  quotient,  ^n  represents  the  relative  lower- 
ing of  pressure  which  will  be  produced  by  1  molecule  of  non- 
volatile substance  in  100  molecules  of  volatile  solvent.  I  have 
obtained  the  following  results  by  making  this  calculation  for 
the  normal  values  of  K,  produced  in  the  different  solvents  by 
organic  compounds%and  non-saline  metallic  compounds  : 


Solvent. 
Water 

Molecular 
weight 
of  solvent. 

M' 
.     18 

Normal  molec- 
ular   lower- 
ing of  press- 
ure. 

K 

0.185 

Lowering  of 
pressure 
produced 
bylmol.in 
100  mols. 
K 
M' 
0.0102 

Phosphorus  trichloride  . 
Carbon  bisulphide  

...   137.5 

...     76 

1.49 

0.80 

0.0108 
0.0105 

Tetrachlormethane 

154 

1.62 

0.0105 

Chloroform 

.   119.5 

1.30 

0.0109 

Amylene  

...     70.0 

0.74 

0.0106 

.    .     78.0 

0.83 

0.0106 

Methyl  iodide  

...   142.0 

1.49 

0.0105 

Ethyl  bromide 

.   109.0 

1.18 

0.0109 

Ether         

.  .     74.0 

0.71 

0.0096 

Acetone 

.     58.0 

0.59 

0.0101 

Methvl  alcohol.  . 

32.0 

0.33 

0.0103 

The  values  of  K  and  of  M',  recorded  in  this  table,  vary  in  the 

j£ 

ratio  of  1  to  9 ;  notwithstanding  this,  the  values  of  — ,  vary 

but  little,  and  always  remain  close  to  the  mean,  0.0105. 

We  can  therefore  say  that  1  molecule  of  a  non-saline,  non- 
volatile substance,  dissolved  in  100  molecules  of  any  volatile 
liquid,  lowers  the  vapor-pressure  of  this  liquid  by  a  nearly  con- 
stant fraction  of  its  value — approximately  0.0105. 

This  law  is  strictly  analogous  to  that  which  I  stated  in  1882, 
relative  to  the  lowering  of  the  freezing-point  of  solvents.  The 

127 


THE    MODERN    THEORY    OF    SOLUTION 

anomalies  presented  are  explained,  for  the  most  part,  by  assum- 
ing that  in  certain  liquids  the  dissolved  molecules  are  formed 
of  two  chemical  molecules. 

FRANCOIS  MAKIE  RAOULT  was  born  May  10,  1830,  at  Four- 
nes,  Nord.  He  was  for  a  time  professor  of  chemistry  at  the 
Lyceum  at  Sens,  but  was  called  to  the  professorship  of  chem- 
istry at  Grenoble  in  1867 — a  position  which  he  still  holds. 

His  best-known  work  is  that  which  has  to  do  with  the  de- 
pression of  the  freezing-points  of  solvents  by  dissolved  sub- 
stances, and  the  lowering  of  the  vapor-tension  of  solvents  by 
substances  dissolved  in  them.  In  addition  to  the  papers  given 
in  this  volume,  the  following  may  be  mentioned  as  among  his 
more  important  contributions  to  science  : 

The  Law  of  the  Freezing -Point  Lowering  of  Water  produced 
~by  Organic  Substances  (Ann.  Chim.  Phys.,  [5],  28,  133, 1883); 
On  the  Freezing -Point  of  Salt  Solutions  (Ann.  Chim.  Phys., 
[6],  4,  401,  1885;  On  the  Vapor -Tension  and  Freezing  -  Point 
of  Salt  Solutions  (Compt.  rend.,  87,  167,  1878)  ;  Law  of  the 
Freezing -Point  Lowering  of  Benzene  produced  by  Neutral  Sub- 
stances (Compt.  rend.,  95,  188,  1882);  General  Law  of  the 
Freezing  of  Solvents  (Compt.  rend.,  95,  1030,  1882);  Deter- 
mination of  Molecular  Weights  by  the  Freezing  -  Point  Method 
(Compt.  rend.,  1O1,  1058,  1885);  On  an  Accurate  Freezing- 
Point  Method,  with  Some  Applications  to  Aqueous  Solutions 
(Ztschr.  Phys.  Chem.,  27,  617). 

Our  knowledge  of  the  depression  of  the  freezing-point  and 
of  the  vapor-tension  of  solvents  by  dissolved  substances,  was 
fragmentary  before  the  time  of  Raoult.  He  was  the  first  to  dis- 
cover the  general  laws  to  which  these  phenomena  conform — laws 
which  have  an  important  bearing  on  chemistry  and  physics, 
and  which  are  especially  significant  for  the  physical  chemist. 


BIBLIOGRAPHY* 
OSMOTIC   PRESSURE. 

W.  Pfeffer.  Osmotische  Untersuchungen,  Leipzig,  1877. 

H.  de  Vries.  Osmotische  Versuche  mit  lebenden  Membranen. 

Zlschr.  Phys.  Chem.,  2,  415. 

Isotonische  Koeffizieuten  einiger  Salze. 

Ztschr.  Phys.  Chem.,  3,  103. 

H.  J.  Hamburger.  Die  Isotonischen  Koeffizienten  und  die  roten  Blutkor- 
perchen. 

Ztschr.  Phys.  Chem.,  6,  319. 
J.  H.  Poynting.      Osmotic  Pressure. 

Phil.  Mag.,  42,  1896. 

Nature,  55,  33. 
A.  Wladimiroff.       Osmotische  Versuche  an  lebenden  Bakterien. 

Ztschr.  Phys.  Chem.,  7,  529. 
G.  Tammann.          Uber  Osmose  durch  Niederschlagsmembranen. 

Wied.  Ann.,  34,  299. 

Zur  Messung  osmotischcr  Drucke. 

Ztschr.  Phys.  Chem.,  9,  97. 

W.  Lob.  Uber   Molekulargewichtsbestimmuug  von    in  Wasser 

loslichen  Substanzen  mittels  der  roten  Blutkorper- 
chen. 

Ztschr.  Phys.  Chem.,  14,  424. 

S.  G.  Hedin.  Uber  die  Bestimmung  isosmotischer   Konzentrationen 

durch  Zentrifugieren  von  Blutmischungen. 

Ztschr.  Phys.  Chem.,  17,  164. 

A.  A.  Noyes  and  C.  G.  Abbot.  Bestimmung  des  osmotischen  Druckes 
mittels  Dampfdruck-Messungen. 

Ztschr.  Phys.  Chem.,  23,  56. 
Lord  Kelvin.  Osmotic  Pressure. 

Nature,  55,  273. 
W.  C.  Dampier  Whetham.     Osmotic  Pressure. 

Nature,  54,  571. 

H.  M.  Goodwin  and  G.  K.  Burgess.  The  Osmotic  Pressure  of  Certain 
Ether  Solutions  and  its  Relation  to  Boyle's-Van't 
Hoff  Law. 

Phys.  Rev.,  7,  171. 

*  No  attempt  is  made  to  give  a  complete  bibliography  of  the  subjects  dealt  with.    Only 
the  more  important  papers  are  cited. 

I  129 


MEMOIRS    ON 


THEOHY  OF  SOLUTION. 

M.  Planck.  Uber  die  molekulare  Koustitution  verdunnter  Losun- 

gen. 

Ztschr.Phys.  Chem.,  1,  577. 

Chemiscb.es  Gleichgewicht  in  verdiinnten  Losungen. 
Wied.  Aim.,  34,  147. 

S.  Arrhenius.  Uber  den  Gefrierpunkt  verdiinnter  wasseriger  Losun- 

gen. 

Ztschr.  Phys.  Chem.,  2,  491. 

Uber  die  Dissociationswarme  und  den  Einfluss  der 
Temperatur  auf  den  Dissociationsgrad  der  Elek- 
trolyte. 

Ztschr.  Phys.  Chem.,  4,  96. 
J.  H.  van't  Hoff  und  L.  Th.  Reicher.     Uber  die  Dissociationstheorie  der 

Elektrolyte. 

Ztschr.  Phys.  Chem.,  2,  777. 

Beziehung     zwischen     osmotischen     Druck,    Gcfrier- 
punktserniedrigung,  und  elektrischer  Leitfahigkeit. 
Ztschr.  Phys.  Chem.,  3,  198. 
Pickering,  Walker,  Ramsay,  Ostwald,  Van't  Hoff,  and  others.     Verhand- 

lungeu  liber  die  Theorie  der  Losungen. 
Ztschr.  Phys.  Chem.,  7,  378. 
W.  Ostwald.  Zur  Theorie  der  Losungen. 

Ztschr.  Phys.  Chem.,  2,  36. 
Uber  die  Dissociationstheorie  der  Elektrolyte. 
Ztschr.  Phys.  Chem.,  2,  270. 
Zur  Dissociationstheorie  der  Elektrolyte. 
Ztschr.  Phys.  Chem.,  3,  588. 

Uber  die  Affinitatgrossen  organischer  Sauren,  und  ihre 
Beziehungen  zur  Zusammensetzung  und  Konstitu- 
tion  derselben. 

Ztschr.  Phys.  Chem.,  3,  170,  240,  369. 
Lord  Rayleigh.        Theory  of  Solutions. 

Nature,  55,  253. 
G.  F.  Fitzgerald.     Helmholtz  Memorial  Lecture. 

Journ.  CJiem.  Soc.,  69,  885,  1896. 


LOWERING   OP  FREEZING-POINTS  OP   SOLVENTS  BY  DISSOLVED 
SUBSTANCES. 

E.  Beckmann.          Uber  die  Methode  der  Molekulargewichtsbestimmung 

durch  Gefrierpunktserniedrigung. 
Ztschr.  Phys.  Chem.,  2,  638. 
Uber  die  Methode  der  Molekulargewichtsbestimmung 

durch  Gefrierpunktserniedrigung. 
Ztschr.  Phys.  Chem.,  2,  715. 
Zur  Praxis  der  Gefriermethode. 
Ztschr.  Phys.  Chem.,  7,  323. 
130 


THE  MODERN  THEORY  OF  SOLUTION 

II.  C.  Jones.  liber  die  Bestimmung  des  Gefrierpunktes   sehr  ver- 

diinnter  Salzlosungen. 
Ztschr.  Phys.  Chem  ,  11  110,  and  529. 
liber  die  Bestimmung  des  Gefrierpunktes  von  verdiinn- 

ten  Losungen  eiuiger  Sauren,  Alkalien,  Salze,  und 

organischen  Verbindungen. 
Ztschr.  Phys.  Chem.,  12,  623. 
tiber  die  Gefrierpunktserniedrigung  verdlinnter  was- 

seriger  Losungen  von  Nichtelektrolyten. 
Ztschr.  Phys.  Chem.,  18,  283. 

E.  H.  Loomis.          liber  ein  exakteres  Verfahreu  bei  der  Bestimmung  von 

Gefrierpuuktserniedrigungen. 
Wied.  Ann.,  51,  500. 

Tiber  den  Gefrierpunkt  verdunnter  wasseriger  Losun- 
gen. 

Wied.  Ann.,  57,  495. 

Der  Gefrierpunkt  verdilnnter  wasseriger  Losungen. 
Wied.  Ann.,  6O,  523. 

M.  Wildermann.  Der  experimentelle  Beweis  der  van't  Hoffschen  Kon- 
stante,  des  Arrheniusschen  Satzes,desOstwaldschen- 
Verdilnuungsgesetzes  in  sehr  verdiinnten  Losun- 
gen. 

Ztschr.  Phys.  Chem.,  15,  337. 
P.  B.  Lewis.  Methode  zur  Bestimmung  der  Gefrierpunkte  von  sehr 

verdunnten  Losungen. 
Ztschr.  Phys.  Chem.,  15,  365. 

R.  Abegg.  Gefrierpunktserniedrigungen   sehr  verdiinnter  Losun- 

gen. 

Ztschr.  Phys.  Chem.,   2O,  207. 
J.  A.  Harker.          On  the  Determination  of  Freezing-Points. 

Proc.  R.  S.,  6O,  No.  360,  154. 
W.  Nernst  und  R.  Abegg.     tiber  den  Gefrierpunkt  verdiinnter  Losungen. 

Ztschr.  Phys.  Chem.,  15,  681. 
A.  Ponsot.  Recherches  sur  la  Congelation  des  Solutions  Aqueuses 

Etendues.     Paris,  1896. 
Ann.  Chim.  Phys.,  [7],  1C,  79. 

F.  M.  Raoult.  Uber  Prazisionskryoskopie,  sowie  einige  Anwendungen 

derselben  auf  wasserige  Losungen.       9 
Ztschr.  Phys.  Chem.,  27,  617. 

RISE  IN  BOILING-POINTS  OF  SOLVENTS  PRODUCED  BY  DISSOLVED 
SUBSTANCES. 

E.  Beckmann.         Studien  zur  Praxis  der  Bestimmung  des  Molekular- 

gewichtes  aus  Dampfdruckerniedrigung. 
Ztschr.  Phys.  Chem.,  4,  532. 
Bestimmung  von  Molekulargewichten  nach  der  Siede- 

methode. 

Ztschr.  Phys.  Chem.,  6,  437. 
131 


THE  MODERN  THEORY  OF  SOLUTION 

E.  Beckmann.         Zur  Praxis  der  Bestimmung  von  Molekulargewicbten 

nach  der  Siedemethode. 
Ztsclir.  Phys.  Chem.,  8,  223. 
Beitrage  zur  Bestimmung  von  Molekulargrossen. 
Ztschr.  Phys.  Ghem.,  15,  656. 
Ibid.,  17,  107. 
Ibid.,  18,  473. 
Ibid.,  21,  239. 

J.  Sakurai.  Modification  of  Beckmann's  Boiling-Point  Method  of 

Determining  Molecular  Weights  of  Substances  in 
Solution. 

Journ.  Chem.  Soc.,  61,  989. 
B.  H.  Hite.  A  New  Apparatus  for  Determining  Molecular  Weights 

by  the  Boiling-Point  Method. 
Amer.  Chem.  Journ.,  17,  507. 
H.  C.  Jones.  A  Simple  and   Efficient   Boiling-Point  Apparatus  for 

Use  with  Low  and  with  High  Boiling  Solvents. 
Amer.  Chem.  Journ.,  19,  581. 
W.  Landsberger.     Ein  neues  Verfahren  der  Molekelgewichtsbestimmung 

nach  der  Siedemethode. 
Ber.  deutsch.  chem.  Gesell.,  31,  458. 

J.  Walker  and  J.  S.  Lumsden.  Determination  of  Molecular  Weights.  Modi- 
fication of  Landsberger's  Boiling-Point  Method. 
Journ.  Chem.  Soc. ,  1898,  p.  502. 


INDEX 


Arrhenius,  Biographical  Sketch  of, 
66. 

Avogadro's  Law  :  for  Dilute  Solu- 
tions, 21;  Applied  to  Dilute  So- 
lutions: First  Confirmation,  Di- 
rect Determination  of  Osmotic 
Pressure,  25 ;  Second  Confirma- 
tion, Molecular  Lowering  of  Va- 
por-Pressure, 26;  Third  Confirma- 
tion, Molecular  Lowering  of  Freez- 
ing-Point,  29  ;  as  applied  to  Solu- 
tions. Gu Id  berg  and  Waage's  Law, 
31  ;  in  Solutions,  Deviations  from 
Guldberg  and  Waage's  Law,  34. 

B 

Bibliography,  129. 

Boyle's  Law  for  Dilute  Solutions,  15. 


Capillary  Phenomena,  63. 
Conclusions    from    Freezing  -  Point 

Lowering*.  88. 
Conductivity,  63. 


D 

Dissociation,  Two  Kinds  of,  55. 
Dissociation  of  Substances  Dissolved 
in  Water,  47. 


E 

Ethereal  Solutions :  Lowering  of 
Vapor-Pressure,  General  Results, 
110;  Influence  of  Temperature  on 
the  Vapor-Pressure  of,  114;  Influ- 
ence of  the  Nature  of  the  Dissolved 
Substance  on  the  Vapor-Pressure 
of,  116. 


Freezing  of  Solvents,  the   General 

Law  of  the,  69. 

Freezing-Point,  Lowering  of  the,  65. 
Freezing-Points,  Effect  of  Dissolved 

Substances  on,  71. 

G 

Gay-Lussac's  Law  for  Dilute  Solu- 
tions, 17. 

General  Expression  of  Laws  of  Boyle, 
Gay-Lussac,  and  Avogadro,  for  So- 
lutions and  Gases,  24. 


H 

Heat  of  Neutralization  in  Dilute  So- 
lutions, 59. 

I 

"t,"  Comparison  of  Results  from  the 
Two  Methods  of  Calculating,  50; 
Determination  of,  for  Aqueous  So- 
lutions. 36;  Methods  of  Calculating 
the  Values  of,  49. 


Law  Relating  to  Dilute  Solutions, 
112  ;  Particular  Expression  of  the, 
113. 

Law  of  the  Lowering  of  the  Vapor- 
Tension  of  Ether,  Another  Ex- 
pression of  the,  119. 

O 

Osmotic  Pressure  :  Apparatus.  5 ; 
Apparatus  and  Method  of  Meas- 
uring, 3  ;  Cells,  Preparation  of,  3 ; 
Kind  of  Analogy  which  Arises 


133 


INDEX 


through  this  Conception,  13;  Meas- 
urement of,  7  ;  Results  of  Meas- 
urement of,  9,  10 ;  Role  of,  in  the 
Analogy  between  Solutions  and 
Gases,  13. 


Pfeffer,  Biographical  Sketch  of,  10  ; 
Osmotic  Investigations  of,  3. 

Properties  of  Dilute  Solutions  Addi- 
tive, 57. 

R 

Raoult,  Biographical  Sketch  of,  128. 


S 

Solutions:  in  Acetic  Acid,  73  ;  in  Ben- 
zene, 78  ;  in  Ethylene  Bromide,  82  ; 
in  Formic  Acid,  77  ;  in  Nitroben- 
zene, 80  ;  in  Water,  83. 

Specific  Refractivity  of  Solutions,  62. 


Specific  Volume  and  Specific  Grav- 
ity of  Dilute  Salt  Solutions,  61. 


Van't  Hoff ,  Biographical  Sketch  of, 
42. 

Van't  Hoff' s  Law,  47  ;  Exceptions 
to,  48. 

Vapor-Pressure :  Method  of  Work  in 
Determining.  97;  of  Solvents,  Gen- 
eral Law  of,  125. 

Vapor -Pressure  of  Ethereal  Solu- 
tions, 95 :  Effect  of  Dissolved  Sub- 
stance on  the,  105;  Influence  of 
Concentration  on  the,  105;  Influ- 
ence of  the  Nature  of  the  Dis- 
solved Substance  on  the,  116;  In- 
fluence of  Temperature  on  the,  114. 

W 

Wullner,  Comparison  with  the  Law 
of,  113. 


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